The BWU has plate mount switches, so you will have to take the keyboard apart and desolder. Seeing as how there's an LED on the switch, you will have to carefully desolder that out first, then the switch you pulled the stem from. After desoldering, you can pull the top housing off the switch, put the stem back in place and solder the switch and LED back in. I would suggest purchasing a brand new switch (usually around $0.68) in case one of the legs on the stem has been damaged or anything along those lines.
I've had this happen a few times before, as I was lucky since the type of switch I've pulled was an MX Black and MX Clear. I managed to shove the stems back in (the lazy way which is more prone to further damaging the switch) by having my cousin help me lightly pull the sides of the top housing with 2 precision flat head screwdrivers while I "shoe-horned" the stem back. While the probability of it working was ok with a single piece stem, it becomes a bit difficult with a 2 piece stem like that of an MX Blue. I wouldnt want something to happen to the white portion of the stem because that's what aids in making the click noise. I highly suggest the desoldering path as opposed to forcibly returning the stem.
Sorry for being the bearer of bad news