No methanol and acetic acid are compatible as mobile phase. Its done all the time.
You may get different specificity with methanol vs ACN, you will simply have to try and see.
Now methanol is slightly less nonpolar than ACN. For the 90% concentration you're at, this is a non-issue, but the usual hint is to increase the concentration by 10 % when substituting methanol for ACN. Maybe you'll need to make your mobile phase 0.1 % acetic in 100% methanol? That won't react either, its been used before.
I'm guessing you're using a typical reverse phase HPLC column in all of my hints. More info would allow more people to help.