You could try turning Character's Visible Off at that point & then re-load Character with new Clothing. So at that point you would have 2 Characters. One invisible & 1 visible.I'm just going to do a quick test & then post a Screenshot.
ADDED - it works.
1st Character visible On. 2nd Characer Visible Off @ Frame 1.
1st Character Off. 2nd Character Off @ Frame 400.