Is the reason because he wanted to fight them without it or because it wouldn't be as effective on them? Or another reason?
Okay, so, after rereading a bit:
It looks like Domina did indeed use telekinesis against everyone he faced up until fighting Mash or his father. The first time was against Cell War, cutting his head open which was presumably done with telekinesis. However, it appears that Cell survived this punishment, and the only reason Domina did such a thing was because Cell had been beaten by Mash during Innocent Zero's invasion of Easton, and thus had to be punished.
The second time Domina used his telekinesis was against the Saint Ars DV candidates, using it to simply slice into their bodied, no headshots here. Then Domina used telekinesis once again to halt Kingruss' Secondth's, so this would been a defensive use before going on to slice into Kingruss' body. Again, this use of telekinesis was only spurred on so that the Tri-Magic-Athalon would only be between Easton and Walkis, giving an advantage to Walkis.
The third and final incident we see Domina use telekinesis was against Renatus and Tyrone who were chasing him, so I was wrong on this front. So during this moment, Domina had used his telekinesis to bisect Tyrone across his stomach and had cut off Renatus' hand. However, this was only the case because Domina was trying to escape from the two, so this wasn't a normal circumstance.
I'm going to say that in this fight, it wouldn't be the right condition for Domina to start using his telekinesis to slash at Shiggy, and even if he did, Shiggy as adaptation and regeneration.