Can I fly the LNAV MDA when the GPS is set up for LPV?
GPS approaches are designed for you to fall back to LNAV if a 'higher' precision option like LPV fails during the approach. Just like going from ILS to localizer only if the glideslope fails.
The Instrument Procedure Handbook p. 4-26 says:

Flying a WAAS LPV approach requires an aircraft with WAAS-LPV
avionics. If for some reason the WAAS service becomes unavailable, all
GPS or WAAS equipped aircraft can revert to the LNAV MDA and land
safely using GPS only, which is available nearly 100 percent of the
time.

So you can just ignore the vertical guidance and fly the LNAV step downs using lateral guidance only from the GPS, and your regular altimeter (not your GPS) to identify altitude.
If you haven't done it already (or recently), I'd suggest practicing it before your checkride to see how your avionics behave. You might get alerts that you have to ignore and they could be distracting. It would be best to get a feel for that ahead of time rather than experience it for the first time with an examiner sitting beside you.
You can also just check with your examiner in advance that they're comfortable with what you want to do.