How do I convert the decimal output of the 7447 BCD to 7 segment
display driver chip to hexadecimal?

You can't, or at least doing so is almost as much work as just solving
the problem from scratch.

There *are* (or at least *were*) binary to hexadecimal display drivers
out there, but even by the mid-'90s it was easier to just program a
small PROM or PAL to do the job (I once sat down and manually
programmed two 32x8 PROMs to do just this!).  Today perhaps the
easiest solution is a microcontroller, which is *massive* overkill,
but easily scalable to implement "fancy" functions.