I'm having a hard time even finding conical, parabolic, or spherical mirrors to purchase...at least ones less than $500. I see a lot of people using such mirrors, but I don't know how to get any that are at least relatively economical or possible to make on your own.
The only one I've seen for sale are quite large (~0.7m in diameter and up), but you didn't say what size and I'd imagine that you'd need something a lot smaller.
Security equipment companies will probably be the best bet.
If all else fails, you could make one, with the help of a local astronomy club.
Either find the sphere/parabola shape you need or heat form it from eg. 1..2mm polycarbonate.
Tape something over the side that the camera will be looking at and make the other side reflective by vacuum depositing aluminum vapor onto it.Small pieces of aluminum is heated by tungsten heaters in a chamber/box while a vacuum is created. and when the aluminum is heated to a certain temperature, normal pressure is restored fast and this makes the aluminum vapor deposit on anything in the box. Star gazers use this method to make mirrors for telescopes, but they deposit on the outer surface, to avoid parallax errors from the dual mirror image of ordinary backside mirrors.
This is a very fragile mirror with zero handling ability, so for regular use you want a backside mirror (and coat the aluminum to protect it).
You can't polish a piece of aluminum to the same degree of reflectance.
I think they use something similar in some (/all) LED reflectors in flashlights, as they're damaged by the least bit of touch as well.
Don't start looking for non-mirrored spheres until you find someone who can "mirror" it for you though.