D&D 5E (2024) Skeleton Familiar plus Net = Fisher of Men

[ECMO3]

would a familiar that has been affected by the warlock invocation investment of the chain master use the specific rule of "Your Save DC. If the familiar forces a creature to make a saving throw, it uses your spell save DC." to override the net save DC with your spell save DC while attacking with a net? it seems RAW at least.

RAW a Skeleton can take the attack action, so it can throw a net.

The save is debatable, but I don't think so. A net is adventuring gear with its own save (based on the thrower's dexterity). I think this would be like using your save DC if it dropped caltrops or used a wand or pushed it into a spirit guardians cast by someone else.