I have used a guy near Bicester who has done a great job of buffing and reconditioning several scotties of mine for a good price <£20. If you PM me i'll give you a link to the site. He should be able to have it good as new.
You could also try a piece of thick card (like off a box)it will take ages and you may need a lubricant so be carfula liqiud polish might do.
We use to use this in the army to polish brass which might be a lot softer than what your putter is made of but i know it used to take out any scratchs
The chap i've used is at customputters.co.uk or something like that. Google that and he should come up. Used him 3 times for scotties off ebay andhe does an excellent job at good price. But send him a photo and he'll give you a quote.
I had a really banged up one obviously from a club thrower, cleaned it up really nicely.
It's fairly pricey, probably set you back around £100-£150 depending on the custom options you go for, but they re-shaft it, re-finish it back to it's "new" condition, and re-grip with a brand new grip and brand new head cover (both of which you can choose)...Along with a load of different customising options (initials engraving, colour fills etc)...So you get quite a bit for your dosh.
I'm lucky enough to be in the position of inheriting mine, so I had no initial outlay, but I can understand it's quite pricey if you've not long paid out for it.
I just mailed th putters to the chap - postage of a golf club tends to run to about a tenner each way there and back. He'll sort out the rust too.
I did have one that I sent back to Titleist for a recondition - came out to £90 but if you drop it off with a pro who stocks titleist there's no postage to pay.