I'll assume you know how to safely remove the strut unit from the car? - by which I mean don't undo the 2nd nut on the damper rod (the one that retains the top mount to the damper rod) until you have the spring clamps retaining the spring. In this case I think you are going to scrap the entire existing strut, spring and top mount so you won't be dismantling the old struts?
So, for you, the dangerous bit is going to be compressing the new spring until it's short enough to allow the new top mount to be fitted. By the way don't compress the spring any more than necessary - it's not good for the spring. If you ever are going to reuse an old spring then be especially careful if it's substantially corroded as this greatly increases the risk of it maybe snapping and the more you compress it the greater the likely hood of this happening. Personally I'd be replacing any spring which looked seriously rusted anyway.
Yes, you'll need a set of spring compressors and they're a very useful thing to have. If you're not going to use them very much - or maybe only think you'll use them this for job - then it's worth asking your local garage how much they'd take to fit them. (I doubt they will lend a tool like this unless you are very well known to them) Replacing broken road springs is such a common job now a days that pretty much any garage can do them with their eyes closed! They may well have a tool like this one:
https://www.onbuy.com/gb/workshops-...I2ZBgggggD4mf5AXLTb7ewWQJQDavKhIaAkiCEALw_wcB Which is "super safe" to use and compresses the spring in just a minute or so. With all new parts and using power tools, I'd be very surprised if it would take a competent man/woman more than a half hour. Some workshops tend to charge not less than an hour's labour for this sort of thing whilst others charge "real time" so it's worth asking around if you decide to go down this route. Just make sure the spring and top mounts are aligned correctly before the top mount nut is tightened.
Another "left field" consideration might be to ask at your local motor factor. Mine have a stock of special tools which they lend/rent to local garages so if you are well known to them they may lend to you. Mine are very happy to allow me to borrow in this way and I've not had to pay a charge yet (although I've got so much of my own stuff I've only had a couple of things from them).
If you decide to buy your own compressing tools then the type Dave recommends above will do the job very nicely, there are many variations on the theme with some featuring retainers so the tool cannot be "flung off" the spring if something goes seriously wrong. Many many moons ago I made my own compressors:
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I've stuck a rule alongside them for scale. I wouldn't want them any shorter than this or you'll not get them onto an uncompressed spring.
When actually using them you must position them exactly on opposite sides of the spring. Then tighten them a few turns, maybe 3 revs? on one then the same on the other. Then go back to the other and go maybe 3 turns again and then 3 on the other and so on until you've shortened it enough to fit. Of course as you tighten one clamp it's going to pull the spring over towards that side. Then as you tighten the other it'll pull it straight again. While you're doing this keep a very careful watch for the spring bending sideways, like a banana? as this will cause the compressor to slip. If it does look to be bending sideways like this then decompress the spring again - a little at a time on each side (the reverse of the tightening procedure) and reposition the clamps. It's a time wasting pain in the butt when you have to do this but don't take a chance on a spring which is not compressing evenly - Road springs are incredibly powerful bits of kit and If a compressor comes off when the spring is under tension it can do a great deal of damage to "squishy" human flesh and bones! I've seen people recommending using 3 or even 4 tools for "extra safety". I would advise against doing this because if you use 4 you'll find that one clamp looses contact with the spring altogether as you tighten the one next to it so it's pointless and if you use 3 then as you tighten one clamp it encourages the other 2 to slip due to the bending of the spring. So, my advice is to use 2 clamps, positioned exactly opposite each other and tighten them just a little at a time progressively.
Another factor worth considering is protecting the coating on the spring, which, if damaged, will allow corrosion to get a hold and maybe cause premature failure at a later date. Professional equipment will come with plastic inserts which stop the coating being marked (although they tend to wear out and get chucked away!) I really like the look of this set:
https://www.ebay.co.uk/itm/183122732775?mkevt=1&mkcid=1&mkrid=710-53481-19255-0&campid=5338785333&toolid=10029&_trkparms=ispr=1&amdata=enc:1WSchVfd6QGiLevUnxQuIjg19&customid=s:GS;gc:Cj0KCQiAjc2QBhDgARIsAMc3SqSm8MAHylhJAFeFvoDy4NdaDQm198QjotjPGjUu_wEn2yQkP-yjzvcaAvPdEALw_wcB Cheaper "DIY" type stuff rarely has refinements like this. When using my compressors I have a couple of strips of heavy duty webbing which I arrange so the spring is insulated from the metal of the compressor.
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The first time I used it I was worried the webbing might encourage the compressors to slip but if anything it actually reduces this tendency and, of course the finish on the springs remains untouched.
I hope I haven't put you off with all the warnings about the clamps slipping and the possible ensuing "carnage". I've changed many springs with these home made tools and never had a single "moment" - just tighten the compressors a little at a time on each one and be very careful to watch for the spring bending sideways. DON'T TAKE CHANCES JUST TO SAVE TIME. A bit of Moly grease on the threads helps reduce the turning effort and prolongs the life of the tool.
EDIT: I would strongly recommend you replace the two bolts with their nuts which hold the bottom of the strut to the hub - They are "special" high tensile steel (not the more usual 8.8 stuff) so buy the right ones.