Cutting strands of wire to fit plug
Yes, it matters a great deal. 

Cutting off extra strands will create a big safety hazard, yes. Yes, it will affect the resistance of the connection.  It will cause a voltage drop and localized heating, which may melt the plug.  It could also cause arc faulting, which could ignite grease or flour residues. 

But also, the plug has a built-in strain relief.  It is designed to clamp #6 cable, not #2.  It won't be able to clamp #2, which in practice means the strain relief just won't be used, and any pulls on the cable will yank on the connections directly.  That would be bad even if the terminations were proper! 

The NFPA and UL don't make these rules to be a pain.  They do it because experience has proven things blow up if they don't.

There are some other problems. Plugs/sockets larger than 60A are very unusual, which means cordage larger than 6 AWG is very unusual.  I have a strong suspicion this is not cordage, but in fact is building wiring. Don't use building wire intended for in-walls or underground, in an application where a flexible cord is normally used. Building wiring can't handle the flexing  and motion of cords.  

Trying to use #2 here is wrong.  Anyone with an experienced eye will spot a #2 cable going to a plug.  They could get written up on a walk-through.  If this shows up in an investigation of an injury or fire, you could really be in the soup, because the boss will swear he didn't tell you to do that. 

I know you have something "on order", but the correct cable is readily available.  It's simply 6/4 or 6/5 cordage (3-phase+ground with or without neutral; number of wires = number of plug pins) and they cheerfully sell it by the foot.  Most likely there's an electrical supply house within 2 miles who stocks it.  

And it's cheaper to boot. Significantly cheaper than #2. 

Super easy to do it right, so do it right.