I have been asked if it's possible to make an emergency key for an F-series, similar to the wallet keys from the e90/e60 generation. I suppose I can distill this question down to this: Is there a self-contained transponder (PCF7936 style) that works on CAS4+ or FEM? I've heard rumors that PCF7939VA works, but I don't know.
I'd love to just cut a generic HU100 blank and toss a transponder in it.

PCF7939 works on Hitag Pro protocol which is the same used in F and G series.
Unfortunately NXP stopped this chipset production since 2011. Which means it is impossible to find it now.
If you did, it will work as you expect.

Thank you. PCF7939VA and PCF7939MA are available to me in large quantities, will these work?

You try, if this chipset supports Hitag pro protocol then sure it will work.