"Not if I can help it" = I prefer not to.
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Darling, will you hold my obviously girly-looking handbag while I make a call.
Not if I can help it.
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Will you run downstairs and get us all cofees?
Not if I can help it.
.
A wish to impose on someone, usually low effort.
A preference to not comply, not have to do something, usually to avoid effort, or entanglement, or similar.