A "true" bonsai is anything woody in a pot.

I would disagree with that definition. A true bonsai is a woody plant in a pot
which has been styled to look like a full-size tree in miniature.

You would have less problem with a wild grape you dug up yourself.

Another solution is to grow other plants in the same family which are
grape-like, but with smaller leaves. Porcelain berry is sometimes used.

Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)