sounds like you'll do fine
read the manual carefully on loader removal. Do it exactly as they say, and watch what's going on as you do it...slowly. Make sure to do it on level ground..or it may even help to be slightly uphill or downhill from the loader...it depends. Probably level ground tho. And try to ensure that the loader does not sink into the ground while its off. Its easy to dent your tractor removing the loader.
The only tip I can give is this; sometimes hoses that have been over a pipe for a long time are kind-of glued to the pipe. You need to break the seal, as no amount of pulling will get the hose off. A sometimes good way to make removal easier is to loosen the clamps (obviously) and then use a pair of channel-lock pliers to grip the hose and twist it. You have to be careful not to crush the pipe, so sharp pliers work best as you don't have to squeeze very hard to get enough grip on the hose to turn it slightly.
That being said, the hoses may just slip off easily, but I sort-of doubt it.
You'll get-er
Remember on installation that you don't want anything to possibly vibrate and wear a hole in your repaired rad. The watch-the-rubber pad was a good tip. Make sure it is in proper shape to do its job. Or buy or fabricate a new one. Inner tube makes good material for stuff...
I looked on tractordata...nice little tractor you got there!
oh, and bars-leak is junk. Silver Stallion is better. The best is coarse black pepper, egg whites or dry mustard (or some combination thereof), although that may cause a problem with your coolant flow through your engine block. A proper rad shop will fix the rad like new. The down and dirty way is to use snips to cut out the fins around the tube/s that are leaking and then pinch them off and solder them shut. You may only have one little leak. I don't know how cool your tractor runs, but many old tractors only need 1/2 of their rad. Your tractor is not old, btw. Just you, lol.
I have stopped leaks in several old rads with kitchen ingredients. And I have used bars-leak too, never very successfully.
Anyway, good luck! You'll be fine. Just be careful with the heavy stuff, like the loader. Or maybe you don't have to take the loader off. i don't know.