I'd stick with a tempered glass mirror.

Your adhesive might stuck to the silvering, but not keep
the glass in place.

If the backing expands or contracts, it might crack the
mirror.

From a safety standpoint, I would use clips or a frame to
hold the mirror in place. A tempered glass mirror would
also be a good idea.

wrote:

with a mirror instead of a piece of glass. Then someone reminded me
that the glass that is normally used for this purpose is termpered.

But, because I would already have to laminate something to the back of
the mirror to protect the silvering, my thought is tempering would be
less necessary. If it breaks, the laminated backing would hold it
together.

Any thoughts on what to use to laminate to the back to protect the
silvering and to provide protection in the event that it breaks? Would
contact cement be safe to use on the back of a mirror?

TIA,
Phil