If an NPC/companion have a weapon that has a strength/skill requirement way above theirs, will it affect them?

For example, would an NPC with a Strength stat of 5 swing slower with a Super Sledge (which has a Strength req of 8 and a Melee skill req of 100) than they would otherwise if they meet the strength requirement?

Yes.

The best way to see this for yourself is to test-drive Boone with the Gobi Sniper and an AMR.
You'll notice that he's absolutely deadly accurate with the Gobi Sniper but has a fairly poor accuracy with the AMR, which is just above his STR level. Veronica will also choose Pushy over the Ballistic Fist, simply because she lacks the required STR to use the Ballistic fist at optimal performance, meaning she punches slower with it, giving Pushy the superior DPS.

Oh okay, thanks a bunch. I use Xbox, and don't have access to PC's console commands.