Making the rechargeable remote is fine. I would probably put a new one in there soon, if it is the original battery. As a side note, do not put regular AA's AAA's or a 3.6 lithium in there, unless you disable the charging circuit on the PCB.
-Mark
You can use a 3.6v NiCd cordless phone battery pack and some longer wires to make a remote rechargeable battery for the MVS system. I recommend the cordless phone packs since they are shrink wrapped to keep them from shorting out. They are also easy to mount with some double-stick foam tape.
Contact Xian Xi over on the neo-geo.com forums. He did a write-up on converting the MVS to use non-rechargeable batteries. There's a resistor you have to remove (480 ohm?) to disable the charging circuit. If you don't, the batteries will rupture and cause a big chemical mess which could eat traces on the board.