Easy job. It's a Carbon Steel head with no over -finish [ like Laquer or Metal Plating ] so easier to do if you have little experience.
If you don't have access to a Dremel and flapwheels, or a grinding machine, take it any good local metalworking shop with a small polishing / grinding set up and ask them to run the rust off with a MEDIUM nylon nylon based polishing wheel then a 1000 grit nylon wheel and then a 2000 grit wheel. Make absolutely sure they protect the shaft as its easy to mark the shaft when trying to de-rust the hosel.
You should get back the head looking a little bit like very finely 'satinised' metal. It does not need to be highly polished. Next do your paint infill and I'd guess you could purchase a small brush / small tin of enamel paint and a small bottle of thinners for $10 ? For absolute 'authenticity' go onto the Scotty website and check the Archive for the relevant paint job. You can get metal marking pens that 'paint' as well and these can make life easier.
Next make sure you remove ALL excess paint and 'laitence' from the thinners. The best way is using a lint free cloth and some pure acetone [nail varnish remover]. Make sure you do this in a well ventilated area as she will not only find out you've stolen her remover but the smell is quite strong !
To 'Black' the putter the layman's way is to 'cold' black it. This is a form of metal oxidisation and used widely on Guns etc., Birchwood Casey make a 'Gun Blue' product - about $12 for a small bottle - and you want the gel one as its much easier to apply. As you start applying the metal will discolour Blue/Black and then black as you apply more. To get a consistent finish you need to work the gel in. Wipe all excess off and allow to dry. You can re-apply more gel if you get a ''patchy'' finish.
Once completely dry ''polish' up a little with a soft lint free cloth then make yourself an Oil Cloth using a lint free cloth and light organic lubrication oil [ we have ''3 in 1'' here which comes in a small 4 oz. tin] Put the oil onto the cloth and wipe the oil all over the Putter surface. You will get a little black on the cloth but that's fine.
Keep the cloth in a small plastic bag in your bag or Car Boot [ trunk ] as you will need it to wipe down the Head after use to keep the finish and assist protection from the elements.
You will lose maybe 5 grms from the metal 'stripping' process and as I refiub around 150 + older Scotties a year [ and weigh most before and after ] the above process should not make a huge difference to the head. You will do more to alter the feel / balance of the Putter by cutting the shaft down and / or putting a different grip on it than the above method and if you can tell the difference then you have better feel than 99% of amateur Golfers in my opinion.
Hope that helps. It's easier to do than it sounds. I actually use a specially formulated cold blacking system and also flame seal the metal.......as well as some other tricks for longevity but that's another story
Best of luck whatever you do.