TRIMMING THE DISPOSABLE RAZOR
Here's what I did, TL;DR: use a Dremel 
As scarf man pointed out a bazillion years ago it feels like, the original razor head looks like it has it's ends trimmed off. The razor's end caps have been taken off on both ends, and you can see the end of one of the two metal inserts. I think the maker misjudged the width of the razor and had to either modify the head or the wooden body to make it fit. The end in the foreground below had to be trimmed for it to fit in it's niche in the body, trimming the other end just cleans it up and makes it protrude less.
RAZOR #1 MODIFICATION:
I'm just going to document this in case it will help somebody else, I don't think it was a great approach but it helped to see how the razor goes together and comes apart.
I went right in with some nips and just snipped the end cap right off. My hope had been that the cap removed would allow the assembly to just pop right apart, but no go. In hindsight, I should have clipped BOTH ENDS and tried prying the top off, but I wasn't thinking.
Besides the endcaps, the razor also has four plastic rivets that are heat-pressed through the two blades and hold the top and bottom halves tog together. I did pry on the halves a little bit, but didn't get much wiggling without the pieces wanting to deform.
At this point I should have trimmed off the other end cap, wedged a micro screwdriver between the two metal inserts and twisted to hopefully pop it all apart clean. NOPE, instead I drilled out the heads of those rivets from the back. It worked, and the head and blades came out.
That was a great victory and the blades are out, but for some reason pretty unsatisfying. I spot-glued the plastic cover back on (no blades), ran a lighter over the cut end to remove the white 'stretch' marks in he plastic, and ended up with this:
WHAT I LEARNED HERE: In hindsight, I would trim both ends, then wedge a blade
between those two metal inserts and try prying the plastic head off. I think those metal flats will likely distribute the force like a big wedge, and hopefully pop the head off clean. Then I'd just reinstall the narrower metal flat into the razor to match the prop, and glue the plastic head back on. One could also just trim both end caps off and leave the blades in, but they are sharp off the ends and I want that bottom blade gone.
RAZOR #2 MODIFICATION:
Common sense to the rescue.... Pulled out my rotary tool with a small sanding drum and went to town:
Maybe a minute, and the cap is gone, no
...Pried between the blades without drilling any rivets, and was successful (kinda). The top did come off, but in the end the rivet heads are just snapping off anyways after a lot of unnecessary prying and bending.
Popped the top off, pulled the blades, put the top blade back in, and glued the plastic top on:
WHAT I LEARNED HERE AND WHAT I'M DOING NOW:
-Dremel is the way to go! It's fast, very controllable, and pretty easy to clean up
-DRILL THE RIVETS, at least two of them... If you look at the last pic above, the blade has dents and the plastic has some stretch marks in it. That is 100% from fighting the rivets and flexing the head when I pried the top off. A lighter run over the top might take the marks off, but I can prevent all of it just by drilling the rivet centers.
-Not a huge deal, but tomorrow I will see if I can flip the installed blade so it is dull-side exposed, or just dull the edge down so it's not a cut hazard. It's not a huge deal, but I could cut myself on a banana and I have a couple dozen more of these razors to deal with
