Higher Math

looks like a straight-edge shaving razor

This is a Habling Rickler. When Raccon skin coats were all the rage you would need to get your great coat 'rickled' in time for the first cold snap. If you didn't attend to the garments maintenence, it would tend to matt and bunch, especially under the arms and in the seat.

When the great depression came people would go without eating lunches for a week rather than suffer the humiliation of having strangers snigger and say 'Getcha Rickle, yer butt's matted!' It is reported that some victims have resorted to suicide.

Something to do with hair - an old straightener maybe.

it's a straight edge razor with a guard used not for thinning sideburns and other facial hair instead of clean shaving.

yeah I agree, some sort of barber tool... at first glance I thought it was an old hole punch but I think that is wrong.

or not...

That's obviously Bender's toothbrush.

Remember kids, theft is the coolest crime there is.

Is it something used in sheep shearing or wool production?

It's obviously an instrument of torture.

Perhaps it's a thinning shear for people with thick hair?

It's a knife sharpener.

Looks like a trousers-creaser.

It's a crimping iron to put waves in hair.

Its a corn dog holder. It holds the sticks while you dip the corn dogs in the oil

It's an old (battery powered) electric hair curling wand. The battery it takes is the width of an AA cell but about as long as a pencil.

Backscratcher.

...I would use it.