Writing from U.K., but anyway:  we purchased a Staywell electronic cat door
about 10 years ago, it worked very well indeed but after about 7 years it
went a bit wonky so it would only work on the backup batteries, not on the
mains.  At the time we installed it you could purchase additional tunnel
sections (each about 4 cm deep) and put them together, so as to make a
tunnel as thick as you needed through your door, that should work for your
wall as well.  Our cats learned from kittenhood to wear collars with the
large "keys" on them (about 1.5 cm x 2.5 cm).  The electronic cat door was
particular about being close to other electronic equipment: computer,
fridge, washing machine, etc., and it would click away when one or other of
the other equipment was running.  We described these appliances as "talking
together".  However, the way it was programmed, it would only accommodate
two cats.

We ended up with three cats last autumn and also a new door, so purchased a
new magnetic cat door, which would accommodate three cats.  They only have
to wear a little round magnetic bobble on their collars.  The door is OK,
but not as resilient as the old electronic door.  There is a local vandal
cat, and he has been able to actually break through the cat door barrier if
he tries hard.  It's as if the little latch isn't strong enough.  If this
continues, we'll probably replace this magnetic door with an infrared one,
which might have a stronger latch on it to keep strays out.  With the
infrared door, I don't like the idea of our cats having to wear a thing on
their collars which flashes all the time.  Unfortunately, Staywell seem to
have discontinued their electronic cat door.  It was fine except as I said
earlier it would only accommodate two cats.

You can try the magnetic door, but if you have neighbourhood vandal cats,
you might have to move up to the infrared model.  You might also like to
Google for a more robust cat door if you're having raccoon problems.

HTHs, s.