Photodiode based trigger circuit

substituting a PT for a PD and how any given circuit may need to change to accommodate that

That would depend on the light levels in your application, on the specific PT chosen, the specific PD, and the given circuit. Consult datasheets for the chosen devices.

can I simply replace the PT with a reverse bias PD?

Perhaps, but most likely not. Phototransistors have gain.

If you have to ask these really basic questions, why try to modify a given circuit, rather than build one that is known to work?