I never owned a MiniDisc player. There are a few cool looking ones, but generally I don't like the curvy designs of this era, with oval tilted buttons and spline-lines. Anyways, I turned the form factor into a handheld... probably a bad idea be be squeezing the disc hatch... the PSP, here for scale (UMD discs were smaller btw.), had the grips to the side of the hatch so it wasn't a problem there. Maybe a regular drive slot could work, with a little dust hatch to keep pocket lint out... if a slot is possible mechanically (all MD players I've seen split open like a clam for some reason *). MD players had a sound buffer (e.g. 10 seconds) so disc shake was less of an issue, but more importantly, the buttons on the device were not necessarily used as the earphone lead often had a remote controller of sorts, sometimes with a rectangular screen, and this further isolated the device from bumps.
*The first MD player did have a regular ejection mechanism, but was quite large.
Square form factor MD players are about 73~76 x 80~82 x 15~20 mm.