A couple of points to consider:
COAL on the 300 PRC max is 3.700", 300 WM is 3.3400" max. Is your mag box long enough to accommodate the PRC? I believe Tikka mag boxes are 3.4" in length.
The case head diameters on each cartridge are identical so if your 300 WM chamber is even slightly eccentric, you'll be oversized for the PRC.
The distance from the base of the cartridge to the end of the neck is longer on the 300 WM than the PRC. One of the benefits of the PRC is the throat dimensions, which will likely be compromised by the existing throat.
After all of this, it still might not feed worth a damn.
