So here you can see it on pic, it has almost same holes as the standard basket but I would like to know your opinions whether it is worth to try it as a cover puck shower despite it has about 1mm or 1/32 inch gap around the sides of the basket. I didn't try it because I reckon it would highly likely push most of water through that gap on sides and effectively underextracting and destroying the shot, or what do you think?

I suspect that 1mm (so 2mm in diameter) is too much, at least for non-slant-sided baskets. I cut down an Aeropress metal filter that I wasn't using and side-channeling resulted, perhaps due to restriction from not enough holes/big enough holes.

Try it and see - the result should show in a bottomless extraction - and taste.