My 2cents:
Working in CV change the first (from the inside): P, Div, H to the designated H# or P. Leave the class intact.
You noticed I included H so the level could be changed H2 > H3
In Sigil, I setup '(wrap with)-Clips for P, Div, H3 complete with any class I wanted to assign (these do not remove any existing tags, only wrap the selection in a tag)
Type some words. Select them. Hit the Clips (toolbar) Menu item
My most used clips are on the clips toolbar