1 - 3/4" wide. That’s only 1/16" more than a GFI duplex receptacle. A Gem box, switch box , with ears would be a tight fit with the dry wall supports added on each side of the box. A GFI duplex receptacle just fits with maybe a 1/32" to spare.
3-1/2" deep switch box with ears.https://www.homedepot.com/p/RACO-3-1-2-in-Deep-Gangable-Switch-Box-with-Armored-Cable-Metal-Clad-Fle...
You might be a little strong on your 1.75" measurement. Surely Furutech wouldn’t make it any wider than a GFI outlet.
In case the electrician wants to install a steel 4" X 4" box with a 1 gang 5/8" raised device cover he would need to cut a hole at least the size of the 4" X 4" box. That would require patching and painting. And if the wall has an orange peel texture you would also have to deal with that too. Nice electrical job though. Lots of room for the electrician to wire the outlet. Not so good for you though....
4" X 4" X 2 1/8 steel boxhttps://www.homedepot.com/p/RACO-4-in-Square-Welded-Box-2-1-8-Deep-with-1-2-3-4-in-TKO-s-25-Pack-823...
1 gang 5/8" raised device cover.https://images.homedepot-static.com/productImages/dfbd6366-dd8c-4eb5-aad8-529f9f1dbb26/svn/raco-cove...
Here are a couple of options the electrician may be already be thinking of. If not you might mention them to him and see what he thinks.
1) A 1 gang 3-1/2" deep steel masonry box.https://www.homedepot.com/p/RACO-Single-Gang-Masonry-Box-3-1-2-in-Deep-with-1-2-and-3-4-in-Concentri...
- The electrician would have to cut the hole fairly tight. Especially the top and bottom of the box. You want to make sure the duplex cover plate covers all the way around the box.
- For mounting the box it would need to be cut-in next to a stud in the wall.
- He would need to drill four 3/16 holes on one side of the box to support the box to the stud.
- Keep the holes near the top and bottom of the side as much as possible. (That way they will not interfere with the receptacle in any way.)
- Front 2 holes about 5/8" from the front edge of the side.
- Next 2 holes about an 1-1/2" back from the front edge of the box.
- Fasten box to stud with four 1-1/4" drywall screws.
A 6" Phillips bit works great chucked in a battery drill for driving the screws. A must for the back 2 screws. (Screws will be installed at an angle into the stud.)
Note all of the above options are steel boxes. In an outside wall a steel box will conduct the cold air inside the stud space even though the wall is insulated. If it gets really cold the steel box may get frost on the inside of the box if the air inside is warmer than the air on the outside of the box.
Next option. Best, JMHO.....
2) A deep 1 gang plastic switch box, at least 20 Cubic Inch. (The deeper the better for the #10 solid wire.)
Example of. 22.5 Cubic Inch. (Buy a good one.) https://www.menards.com/main/electrical/rough-electrical/junction-boxes/legrand-reg-slater-reg1-gang...
- The electrician would need to cut off the existing plastic nail supports on the top and the bottom of the box.
- Install the box in the same manner as the masonry box.
Again, cut the hole for the box fairly tight. Especially top and bottom.
- Drill holes near the top and bottom side of the box.