I was taught that the outside foil (bar marking) should go to ground or to the lower DC potential as a safety matter. The older capacitors had just paper and wax outside of the outer foil, so it was not wise to connect +300 V to that end. Since then, there have been silly postings in audio literature about the direction of signal flow, etc. Of course, there is capacitance from the outer foil to ground (if neither end is grounded), but is much smaller than the actual capacitance of the capacitor so the effect on shunt capacitance from the signal node to ground is negligible.
However, it is definitely a good idea to replace non-hermetic paper capacitors of that vintage, since they tend to absorb moisture over the years. Following such advice, I replaced all the similar plastic-cased capacitors in a Tektronix 130 L,C meter with modern polypropylene foil units. Measuring each original capacitor after removal showed bad Q values on each.
For a VTVM, I think the discrepancy between 0.005 and 0.05 uF is not important. You may find it easier to buy 0.047 uF.