You should not need a grounded chassis (radio metal case) besides any already designed into it from it touching its internal circuit ground from a PCB or ground strap. If the wiring harness ground leads are good it should work.
There should be at least one, probably two ground wires coming from the factory wiring harness. It might help if you dug up the wiring diagram for your '95.
Did it have the stock radio still, or at least an unmolested wiring harness? If so, which radio did it have? AFAIK your 4 choices are:
1) Base Radio
2) With CD Changer
3) Premium MACH sound system
4) Premium MACH without CD Changer
Tell us which of those 4 it is and I probably have a wiring diagram for it.
Edit: There may be a 5th variant of those listed above, you could just post the wire colors on the harness you have, either in correct pin order or also post a picture if you don't know which of the radios you had.
Anyway you'd set a multimeter to 20VDC range (or the closest range over 14.4V, 100VDC range would work in this case), put the multimeter red lead on each of the two power leads in turn and the black meter lead on any chassis ground point to verify that both power wires have ~12V+ on them. The clock/memory power lead will have power at all times. The stereo "on" power lead will only have power with the key in the run or accessory position.
Next you can use the multimeter to check whether there is continuity (or very low resistance) between the (probably two) ground leads and any chassis ground point (unpainted metal, bolt head under dash, etc).