Probably a little late but may help someone else with this question in the future. In my experience there are at least 3 generations of the Canonet QL17 and I can say this with certainty as I own all 3 versions.
1st Generation
This one uses either a Mallory Mercury RM-1R, or a National/Toshiba TH-MP batteries that are no longer available. These batteries are ~9/16" dia x 5/8" tall. The best solution I've found is to either purchase a $40 adapter from
http://www.smallbattery.company.org.uk/sbc_mr50_adapter.htm or use the later 625 battery (see below) and include an aluminum spacer. That's what I'll do once I buy an earlier QL17 that works unlike mine which has a stuck aperture/shutter.
2nd Generation
This one uses a National M-1D, Toshiba TH-MC, Mallory RM-625R, Eveready E625, GE#625, or Burgess Hg 625R batteries. Unlike the earlier models batteries, these are about ~9/16" dia x 1/4" tall. (i.e. a lot shorter than the earlier model).
3rd Generation
This one is what most refer to as the G-III also uses the same battery as the 2nd Generation model
Like I said I own all 3 of these models.
HTH!