See my previous question here.

Let $M$ be a smooth closed simply-connected $4$-manifold with $w_1 = w_2 = 0$. Can $TM$ be trivialized in the complement of a point?

This was answered in the affirmative.

My question now is, is it possible to conclude in some way from Smale's immersion theorem or something similar that $M - p$ admits a symplectic structure, where $p$ is a point?