I strongly recommend using Eneloop batteries with factory-attached metal tabs. I got mine for less than $3 a piece, and they make the process much easier. Just be super careful and do not touch these tabs against each other, or it’ll result in a dangerous rapid discharge. Because of that, in order to be safe, get a pre-built 2-pack or add some insulation for the duration of replacement. Don’t even try “being careful” - you’ll touch them.

If you got them separately, you’ll want to salvage the bridge from the old set, as in step 8, or use a metal wire to connect them.

While the batteries themselves fit without any issues (I think I had a newer shaver revision), connecting them just as the original ones required very flat solder joint. It may be easier to keep the bridge above or below batteries, rather than at the end.