I think the OP may have a validly odd battery question he's asking.
If the battery in his picture came from that Canonet QL17, what is it?
It's not a PX625 format. It's much too tall for that. (I have a QL17 GIII and a freezer full of 625 mercury cells.) But references I've looked at, including Canon's historical archives, says 1.3-volt (MP) mercury. And he says the compartment door reads 1.3-volts.
The only form factor I could find that matched that voltage, used to be available in mercury, and looked similar was a PX640. But even that seems just a bit shorter. And nowhere could I find a reference to 640s in Canonets.
There is the PX27 format, but I believe the voltage is incorrect (5.6-volts in the original mercury version), even though it closely resembles the photo.
So what is that battery?
(Regarding camera model, I also note that his lens collar levers are significantly different from other QL17s.)
[Edit: See the following link for an excellent Mercury Replacement Battery Catalogue by the Small Battery Company in the UK.]