Learn English – “Wait with doing something” grammatical

My preference would be to use the combination "wait on" to mean to delay or to put off for a duration of time.

Using wait with does not imply a delay I don't think.

"Wait to" doesn't imply the active intention of causing a delay I don't think. I'm going to look more deeply into this. For now I found the following from Mirriam Webster online:

Mirriam Webster online - Can wait on mean ‘to wait for’?

American dialectologists have evidence showing wait on (sense 3) to be more a Southern than a Northern form in speech. Handbook writers universally denigrate wait on and prescribe wait for in writing. Our evidence from printed sources does not show a regional preference; it does show that the handbooks' advice is not based on current usage. ⟨settlement of the big problems still waited on Russia — Time⟩ ⟨I couldn't make out … whether Harper was waiting on me for approval — E. B. White⟩ ⟨the staggering bill that waited on them at the white commissary downtown — Maya Angelou⟩ One reason for the continuing use of wait on may lie in its being able to suggest protracted or irritating waits better than wait for. ⟨for two days I've been waiting on weather — Charles A. Lindbergh⟩ ⟨the boredom of black Africans sitting there, waiting on the whims of a colonial bureaucracy — Vincent Canby⟩ ⟨doesn't care to sit around waiting on a House that's virtually paralyzed — Glenn A. Briere⟩ Wait on is less common than wait for, but if it seems natural, there is no reason to avoid it.

Further down this same page the combination "wait to" is shown but I don't think this reflects the meaning you are seeking to convey:

I know she was happy when I lost my job. She was waiting to see me fail.