http://wiki.eveonline.com/en/wiki/For_the_State_%28Chronicle%29At least some Caldari use man-portable railguns. Remember, hybrids are not just plasma weapons. As for railgun power sources, I find it credible that they could be powered either by a "central battery" in the weapon itself. Or then have a heavy backpack power source, possibly with just a capacitor in the railgun itself. Or then have capacitors in the rounds themselves. (The rounds would likely be not-charged during transport and storage, and recharged before loading the weapon.) It is notable that the EVE weapons are, as far as I am aware, actually coil guns, but regardless of the actual mechanism, they'd likely require serviceable parts (either the barrel or the rails) if we'd go with full realism.
Gallente blaster-type hybrids (particle accelerators) don't make much sense in athmosphere, perhaps they could be made some kind of a "shotgun" or "flamethrower" type weapon, short range but you don't want to be there.
As for Amarr weapons, rechargeable batteries on weapons, power packs or power plants carried on backpacks or discardeable batteries all would work within reason. As noted, there could be both interchangeable lasering units ("crystals") or fixed-wavelength weapons. The scientist in me wonders about the precision of removable crystals when serviced in field conditions, but I guess that is a non-issue at infantry combat ranges (slightly greater for snipers etc.)
And finally, it'd be quite interesting to see electrolasers. A high-power beam causes blooming in the medium, which causes it to disperse and lose power. The solution is to ionize the medium and then send an electric shock during this conductive channel. (Artificial lightning, if you wish to see it so.) Of course, another solution is simply to use pulse lasers with such of a short pulses that the blooming effect is avoided. A yet more technical solution is to monitor the dispersion of the beam and then adjust focus to avoid it.