With some pondering, and a wee bit of knowledge gained looking over the shoulders of men who could solder a splice case onto lead shield, it could be either a cutter or a shrinker depending on the ability of the splicer using it. Unfortunately by the 60s lead was being phased out of overhead, and those pliers look a bit small for subway.
Best I can think, (sit back down Rusty) they might have been used to seperate a rotted case from the cable more or less in the manner of a tubing cutter. Knowing Ma Bell there might well have been a bucket of money invested in crating them to prevent a splicer from damaging the paper insulation with his saw and splitting knife. That combination probably created a lot of LONG splice cases.
I can also see it being employed on a new splice, where 2 cables join rather than a midspan to squeeze down the end of the bell into contact with the cable. After all, solder will only span a gap of about 15 thousandths of an inch.
All in all I don't see much of a production run on that tool. Nobody was going to haul it up to a platform when a hose clamp worked better.
