Before you even do that, you might save some trouble with the soldering and repacking by testing them in pairs, in circuit.
The way I would do this is to set a pair at a time on a CV supply of 4.2V and connected to an ammeter. If you have a lab supply, just use that. If the current doesn't eventually trickle down 0mA to 1 significant digit, or at least under 10 mA, then at least one of the pair is bad. A bad 18650 cell will generally suck over 20mA, indefinitely, at 4.2V. Possibly a few hundred.
is it more likely that a cell is completely kaput?
This is highly likely the case. The weakest link is what kills the battery. Just a matter of what is the easiest way to verify that, for you, to do the simplest repair.