A small sling bag or backpack.

But specifically one whose compartment pulls open completely flat and without having to fumble with undoing individual zippers. Just grab a flap or pull-tab and yank, and the entire safe is exposed for rapid access. (Though you may have to come up with a strapping system to keep the safe anchored, using something like adhesive velcro strips or similar.)

I know Vertx and 5.11 offer/offered bags like this, and I'm sure there are a number of other manufacturers offering similar.

I have a Vaultek Life Pod that I carry in my old CPAP travel bag. I can also throw a couple holsters, mag pouches, knives, flashlight, etc. The CPAP bag doesn’t attract any attention (that I’ve noticed anyway).