Hi Dima, beautiful paint job there, and such a tastefully dignified colour!
The gear lever is moulded around a plastic ball which is, in turn, moulded to the end of the lever. The whole lot is completely un-removable and you will end up cutting it all to bits... also, there are slightly different mouldings for the different trim levels. Yours is a Mk1 45, so the knob is a one-piece affair (the 70 models had a separate disc pressed-in with the shift pattern).
Basically, if you don't like it, just take a hacksaw to it. Make a vertical cut from the top, and when you get to the metal, prise the remains of the knob off with a screwdriver. Bear in mind that someone, some day, may like the original knob back, so you might like to grab a spare from a wreckers and demolish that! Also, fitting the replacement gives you an opportunity to tackle the bush halfway up the lever, which is a common slackness point. Some extra washers and possibly the new bush kit (cheap from your FIAT dealer?) will make a big improvement.
The handbrake should have a plastic grip with ribs on top and finger-indents underneath. If yours has come off, you probably want to replace it with a general do-up part from Halfords. Usually they clamp onto the handle. Be aware that if yours still has the plastic grip, that may also be almost impossible to remove! And so again, you'll end up cutting it off.
It's normal on the Uno for the handbrake lever to be exposed - there is no gaiter as standard, though the carpet has a reinforced rounded hole which might be suitable.
If it's any consolation, the handbrake lever on the Uno has the same grip as fitted to a Ferrari 308GTB/GTS... so I personally wouldn't bother changing it, but in the name of style... it's up to you
It's the same on my X1/9 as well.
Cheers (and welcome!)
-Alex