[Chas]

Can I use the .01 safety caps to replace the .25 caps or should I order the larger value safety caps?

Yes, the .01mf is sufficient bypass without having an excessive AC line current pass-through. A higher value of .03mf could, with other equipment on the same GFI branch circuit, cause a nuisance tripping of the circuit breaker.  The OEM value of .25mf is extreme by todays standards. Such a value even with NEW "Y" capacitors would give an uncomfortable tickle and under certain conditions a disturbing shock, if accidentally combined with another device in use the shock could be very hazardous. For the VTVOM it could make low level AC voltage measurements impossible.

I do not know the instrument being repaired, if it has a power transformer, the windings can be leaking to the core. That would be a problem, an open style transformer can be disassembled and the core more effectively insulated to reduce the shock. However the primary could be leaking to the secondary and often that is in direct reference to the chassis. If so, then the transformer would have to be replaced.

YMMV

Chas