There is a saw that will cut in tight places, but it is not a
woodworking tool, it's a medical tool for cutting bones and the like.
As a past orthopedic PA, I became aware of its use for some
wood-working jobs in very tight places. These operate by compressed
air. Here is a link to one type of saw:
Do a search for orthopedic bone cutting saws and you will find other
companies that make these saws. I thought Midas Rex made these, also,
but I didn't see any on their site. Ebay may have some used ones, but
these are outrageously expensive.
Also, a cast cutting saw will work the same way and may be much
cheaper. A cast cutting saw is also a reciprocating type saw. It
usually has a circular teflon coated blade, but bone cutting type
blades can be installed on it, allowing for getting into tight spaces
for cutting. I have a used one (we had in our medical office) that we
replaced because a bushing wore out (which I fixed). I have reason to
use it, maybe, once a year. Twenty years ago a Stryker cast saw with
vacuum attachment went for about $200.00. I see today (I just did a
search) just the saw, new, is about $900.00. WOW, that's some
difference! Maybe a used one can be found on Ebay for a reasonable
price. I should go into business reparing broken ones. They are easy
to fix, few moving parts, etc., but alas I'm retired, so.....
I dare say, I doubt if my post is encouraging for you, with these
prices noted. Maybe there is a similar tool, for woodworking (that I
am not familiar with), that is more cost effective.