If you want to change everything to map units you can open the project in a text editor and do a find and replace:
Find:
v="MM"
Replace with:
v="MapUnit"
If it's just for one layer. Find the section in the project file that controls that layer. Easiest with the layer name.
Search for:
<layername>your_layer_name</layername>
Just above it will be a maplayer tag:
<maplayer simplifyAlgorithm="0" minimumScale="0" maximumScale="1e+08" simplifyDrawingHints="0" minLabelScale="0" maxLabelScale="1e+08" simplifyDrawingTol="1" readOnly="0" geometry="Point" simplifyMaxScale="1" type="vector" hasScaleBasedVisibilityFlag="0" simplifyLocal="0" scaleBasedLabelVisibilityFlag="0"\>
Which will end with an end tag:
</maplayer>
So replace all the references within those tags.