I've done this on several occasions and it really worked well for me. I used the day off mid-week to do all the home chores that normally ate up part of my weekend (cleaning, laundry, small home repairs), which meant that my weekeneds felt a lot more free. It also meant that I could go shopping mid-week without crowds, which resulted in a sizeable time-savings.
I will say it's not for everyone though. The added hour can feel enormously long until you get used to it, and depending on what your employers expectations are, it can be difficult to match the productivity in 4 long days as you get in 5 slightly shorter days. I've even seen studies that suggest that working 6 days of 5 hours yields about the same productivity as the typically 4x8hr, despite fewer actual hours worked.
IF you have a choice, take Wednesday off.
Why Wednesday? I have had every other Wednesday off, so I would likely keep that, but was thinking that Tuesday would be smarter if I got to pick. My thoughts were we are closed for the Monday holidays, so if I have Tuesday off, I get a 4 day weekend without requesting it.
Well you said you couldn't take Monday or Friday off to give a 3 day weekend, so that was out.
For me personally, taking of Wednesday was the most relaxing. It meant most weeks I had two days off (weekend), worked two weeks, had a day off to 'do everything' (laundry, errands, cook, clean etc), then two days off before the weekend again.
Taking off a Tuesday meant I was working just one day after a weekend before my next day off, then three days in a row. By the time I got to Saturday I had a list of tasks to do at home that ate up my entire Saturday. Thursday is a bit better but still not very balanced.
Yeah, taking tuesdays off can be nice when you have a 3 day weekend (making it a 4 day weekend), but those are few and far between - something like 7 or 8 per year. The other ~40ish weeks I'd like the break mid-week. Plus you do get a bonus on Thankgiving of a 5 day weekend.
Just my experienced and preferences.