What's the best way to fix skirting board without nails / screws?
Well, you could form the skirting directly out of plaster, but that would only fulfill the "appearance" and not the "function" (such as it is) of the skirting board. And for most of us that would be more "messy" than "elegant", though the real plaster pros can do very elegant things in the high side of the wall for moldings that won't see the abuse a skirting board will.

Wedging is probably the best way to do this - rather than tryng to get "precise" lengths across, if you can get a pack of tapered shims (narrow wooden shingles) you can use a pair in opposite directions to make a wedge-clamp arrangement on studs just a hair shorter than the width. Drive in the wedges to tighten.

I'm not familiar with your brands, but if it's a good quality polyurethane construction adhesive, once cured, it should stay put.

When in doubt, leave it clamped longer. When not in doubt, leave it clamped longer anyway. An extra day or two of stepping over clamps is not nearly as inconvenient as trying to do it over...