Hi Nicola,
Provided the paint hasn't dripped inside the locks a simple metal paint remover on a cloth on the outside can be used.
If it's inside the lock and affecting the use of the lock then calling a local locksmith would be the best idea.
The pins can be difficult to control once the plug is removed without the correct tools. The plug will have to be removed to clean it out properly from the inside.
Hope this helps.

The last answer to this question is referring to a rim cylinder. A rim lock doesn't have pins!!!
It can be taken apart and cleaned.Most old rim locks have been locally manufactured and no parts are normally available but if you have a good locksmith he should be able to repair/ replace or get locally manufactured the parts you need.
If you have lost the key this can be more difficult but still do able if you pick someone with abit of knowledge about cutting keys.
I have done one not so long ago, I repaired it in my spare time from a grade 2 listed cottage and cut a key as the original was lost it is possible but takes some time getting the key cut correctly. Can also be quite costly.
My local iron munger makes old rim locks and are a cheaper alternative and still look original to the buildings features.
Kind regards