Cutting a portion of the under part of the hood will not effect the hood at all.
Anyone who tells you otherwise is wrong.
To cut a small section wont hurt. But to cut alot of that meshing off and over time the hood "MAY" deform... but its doubtfull.
My civics was fully cut except to reinforce where the latch is.
Its still metal remember and its still strong. It wobbled around when you closed or open it but ... but deal...
What you suggested though in your post would not harm your car at all. You could cut all around where the bar is.