Another alternative is to handle WM_NCHITTEST. In it call DefWindowProc to get the current hit-test value, if it's either of HTRIGHT or HTLEFT then return HTCLIENT or HTBORDER and the cursor won't change to the sizing one, thus disabling it.
This seems quite kludgy.

If I go to the Menu in the upper left (Alt+Space) and hit resize, does it still prevent me from resizing? I'd almost bet not, but I'm in Linux at the moment.