Two things I've been asked a few times now are "How do I get a smaller diameter watch battery to fit in a larger hole?" and "How do I make up the thickness for thinner watch batteries?"
Well my advice is, usually, try to get the correct diameter battery as the thickness can be made up easily from folded kitchen foil etc. I then give a few ideas on what to do if the correct diameter is not available, here.
I did come across the problem myself of not having the correct diameter battery for a watch. I had purchased one of those "battery cards" that has 30 watch and calculator batteries of various sizes, because I needed an SR44 for my electronic vernier, plus an AG4 for one watch and an SR626SW plus an LR1120 for another watch. I didn't have the Button & Coin Cells Equivalents page with me so I just hoped that the sizes I required were on the card (I knew 2 were, I was pretty sure another was too!) and, as the card of 30 batteries only cost £,1.00 I took the chance (I had seen SR44s marked up at over a pound each in a supermarket and there were 6 on the card!).
On my return home I fired up the PC and checked the batteries I needed against the ones I had. Very soon my vernier was working without flashing at me and a 1996 promotional watch (from Mars, the sweet people, not the planet) was working fine again too.
This left the Philip Persio dress watch, which needs 2 batteries; one for the analogue movement and another for the digital and alarm side of things. A quick check and the correct one fitted to the analogue movement had the hands moving again. The LR1120, required for the digital and alarm, didn't have a match in the selection. The closest to it was the correct diameter but twice the thickness. I did try it just in case, but I would never got the back of the watch refitted. I then checked out the specs for the other batteries in the selection and found the correct thickness but the diameter was about half of what was required.
Mindful that the volume (therefore size) of the battery denotes its' capacity and the fact that a battery half the size will last approximately half the time of the full sized battery (I'd had the watch for 3 years and it only just needs a battery), plus the fact that I don't use the alarm or the hourly beep functions, plus the fact that I had so many batteries for so little money, I decided that I would go ahead and fit the smaller cell.
The battery is only 2.1 mm thick so I needed something thin, conductive, pliable enough to shape but would hold its' shape on its' own. As my eyes wandered around the shack they settled on a roll of solder. It ticked al the boxes for me so I wound some solder around the smaller cell, using the expired larger one to check for size (image 1 below). I then took the coil of solder and dropped it into the battery compartment, checking it for fit and that it made contact with the side terminal and than dropped in the smaller cell in the centre (image 2). I refitted the battery retainer (image 3) and checked the digital display to make sure all was well (image 4). The back was replaced, time and date set and my dress watch was now ready for use in time for the Radio Club Christmas Party.
I hope that this article has given you some "food for thought". The method and materials can be adapted to whatever you've got available. For example, if I'd spied some stiff copper wire I could have used that (not stranded type, whiskers will cause short circuits). Brass or aluminium strip perhaps, or even kitchen foil folded a couple of times to make it thicker then wrap that around.
This is not advised for high current applications as the smaller battery will be exhausted quickly!