Dear Jake,
Ah, sorry I overlooked the fact you said you wanted to do the SCDM with VASP -- I was focused on whether or not you could do SCDM at all.
Yes, this will be an issue, because the Koopmans calculations that follow the Wannierization are performed in QE, and they will need to read in information from the preceding DFT calculations such as the wavefunctions (in QE format) in addition to the Wannier90 files. You do not want to mix-and-match Wannier90 files generated from a VASP calculation with wavefunctions from QE, because applying the U matrices from VASP+W90 to the KS states of QE will not give you MLWFs.
I am not familiar with W90 + VASP, but performing SCDM with W90 + QE should not be too different.
Best wishes,
Edward