I also think it culd be a 54mm diameter male size emitter.
It makes me think the saber is probably used on death star, and would be the saber with the cone, because the weird grenade seems to be on that saber, and the emitter diameter looks a bit smaller too you can check there are two sabers here, I mean on the grey background views, one of them looks like the archive saber, with slope on grenade body and back hollow emitter core, and another with emitter cone, "looks like a weird" grenade, and "would be smaller, yes, but no way to get sure it's a male" emitter.
I think it can be possible some males to have a slope on the back, or females to be smaller, because nobody get enough loose parts and made enough comparations to get sure the models had unique design, as for the grenades, and the 4 emitters I get in hands have shows sone later modifications, especially on front, where there was some shiny areas and other weathered from older machining, there were also hand engravings on all emitters.