Hey Fedox! I don't have a whole lot of experience mapping, but I have some advice that could possibly help you.
First thing I would try (If you haven't already) would be BSPSource. It's a very common decompiler that should have an option to bypass IID NoDraw when you turn it into a VMF. Under the "world" tab, you should be able to set the mode to "Original/Split Faces". It will give you the correct textures, but the brushes will be a little wonky and you will have to fix some of them. After you do this though, compiling the map will be a pain in the ass, borderline impossible apparently.
The other option that could help you out is EntSpy. Using EntSpy, you can remove the "no_decomp 1" flag before decompiling. This could solve your issue, but it could also break some things, so I would make a copy of the BSP before doing so.
Then again, I do not usually do mapping and generally only do it when I want to edit something on a map that has been made for one of my communities. The advice above is a combination of my personal experience and web surfing. I hope this helps!