The term "have a hand in" refers to participating in or having influence over a particular situation or project. Antonyms for this phrase could include "stay out of," "avoid," or "abstain from." If someone wishes to distance themselves from a project or avoid getting involved, they may choose to say they will not have a hand in it. On the other hand, if they intend to fully commit and be an active participant, they could say they will be heavily involved and will have a major role to play. Ultimately, the choice to have a hand in something or not is up to the individual, and they may use different antonyms depending on their desired level of involvement.