This is not good. No, not at all good.

A speaker cabinet is not simply a box that holds the speaker. It is a
finely tuned accustic instrument. Can you determine what the outside
surface of the cabinet is made of?  The outside of the box is
unimportant to the sound, it is finished only for looks. It is the
insides that determine the sound. They are never made of solid wood,
it would warp and they must be air tight.

There are some that are all plastic inside and out. These are really
bottom of the line units, but the plastic will tolerate lots of water
and some strong solvents, mostly water based. Plastic will not
tolerate petroleum based solvents. Some will instantly disolve some
plastics, so be carefull. For example, acetone will disolve
polycarbinate like heat melts ice.

How old are they, roughly. How much did they cost, roughly. What I am
looking for it quality. If they cost $5US a couple of years ago, they
are not worth much effort and may be very fragile. If they cost $1000
twenty years ago, they are very high quality and are worth doing a lot
of cleaning.

The good ones are usually plywood or particle board covered with real
wood laminate or with vinyl that looks like wood. I have seen some
that are covered with a plastic laminate. Laminate can tolerate a lot
of water on it, and several kinds of more agressive (hotter) solvents.
Vinyl, like contact paper, can tolerate a fair amount of water and
solvents that are a little hotter than water.

Real wood laminate is the least tolerent of all to water. It is
tolerant of some hot solvents, but others are instant death because
they disolve the glue that holds the wood laminate on. Painted ones
are like any other painted surface, a little oxi-clean in warm water
will usually do the trick.

Lastly, there are some that are made of aluminum. These are usually
painted or go through a chemical coloring process called anodizing.
They are very tolerant of most water based solvents and many petroleum
based ones.

With any solvent, be careful and test a small spot before parts that
are to be seen.