Would I be able to use a rechargeable battery in a Fluke 87V (based on specifications)?
The Fluke 87 User Manual specifies the compatible batteries as NEDA 1604,
6F22, or 006P. A cursory search turns up Lithium-Ion batteries in the 6F22 format. So, yeah, those type should work.

Many primary batteries have a rechargeable equivalent. Either through stacking cells or internal voltage regulators. The main thing to avoid is placing primary (non-rechargeable) batteries into devices that expect rechargeable batteries. The other-way-around is usually more forgiving.

In general you need to meet the voltage, meet or exceed the current rating, and ideally exceed the capacity.