The most common tool used for reaching into cylinders is a dental drills as you can get them relatively cheaply from china and they are all over ebay. They are small and easily fit in the spaces requires. The only potential downside is the bits need to also be small, so it takes a measure of patience to get the result desired. On the plus side,that also means it's a lot harder to screw up.
An example here.
Another option that is a bit more expensive is a right angle pencil die grinder. Normally priced around 170-200 bucks, but Napa has one on sale for just $45
Napa grinder ( just bought one because that deal is just too good to pass up.)
Obviously, you will need a compressor to un it as it is a pneumatic tool.
There are also electric right angle mini drills out there, similar in size to the pencil grinder, but more expensive and a bit more clunky. Most of these are around $300 and go up from there. They come in electric and pneumatic.
This is a pneumatic example.