Definitely possible at home. The odd ball and special radiators I have been doing myself for over 30 years now, you don't need much more than a gas blow torch, however you do want about a 30 - 35 mm dia nozzle for it, not that you need (or want!) a hot flame, but a broad flame. You'll also want a means of holding the radiator, I current use a 'workmate'. one of the small fold up benches for builders, that has the long clamp up top
Some paste type fluxes, 3 - 4 mm solder, I prefer then non fluxed type and for some of the repairs, I also use Plumbing Metal, which is similar to solder, but more like plasticine, the old school body guys also use this as body filler.
The metal sides are soldered and riveted on to the header tanks. I usually find it best to linish the heads of those rivets off rather than trying to drill them to get it apart. After linishing, just warm them a bit to melt the solder. They are riveted as solder alone is not nearly strong enough, especially with vibration, to hold them together. Look around for some copper or monel pop rivets to use for re-assembly. Try the smaller ship chandlers or plumber's suppliers as they usually have them in small packs of 10 or so as they are dear and it's unlikely you'll go through a box of 1000!
Don't get the parts any hotter than needed for the solder operations,
Have some practice goes at soldering. This type of soldering, while the same in principal to doing say wires, is vastly different in practice!
Be sure everything is really clean before trying to re-solder. I start off wire wheeling them, then use steel wool. For the really grubby stuff, I put them in the acid to clean them up.
I made up a plugs for pressure testing from some heater hose, a bolt, washers and a nut
Or there are commercial types available, but I find the home brewed ones better
Fit a blanking ca[ and then use a hand tyre pump on the over-flow outlet to pressurise it to check for leaks, though these days, I I have a commercial type tester / pump.
Don't expect your first to be a success, however, it will be rewarding
