Hi there, specialist doesn't mean special weapons - that's a common internet houserule but not what the term actually means.
Instead it means if it upgrades instead of rolling on the ganger chart, it picks from the hero chart for advances. It could be an aberrant becomes a champion (an abominant example, you might say), and then do post-game actions. But the rules do NOT mean it takes special weapons - it is limited to its entry options unless your arbitrator says otherwise.
If you want clarity, check with you arb foremost to clarify things what they mean by specialist in the context of the campaign (is that a restriction on special weapons, etc), whether you can start with an aberrant rather than a neophyte as a specialist, then can aberrants become champions if they roll right, etc.