Hello Anon! Ahh in my opinion, it’s just simpler than that. 

There are two kinds of beherits, the ‘normal’ type (that Guts is carrying and that Puck calls his) and the crimson type (that Griffith had) and that is for the five evil angels of the God Hand. However a beherit is also defined as such:

and in my opinion, that’s why the Skull Knight can’t use the one that Guts is carrying, because it has yet to be used and lead its true owner in front of the God Hand.

You heard what Flora (and even Gedfryn) said, if a beherit doesn’t belong to the one who’s carrying it then it’s bound to leave its carrier at some point, which is probably why the Skull Knight never bothered with Guts’. 

All the beherits that the Skull Knight took were from Apostles specifically as you pointed out, but it’s also true that Apostles already used their beherit and sacrificed their most precious love.
So in my opinion, that’s because the beherits that the Skull Knight is using already served their purpose that he can turn them into his special weapon (because they’re still fetishes opening a road to the abyss).

TL;DR it’s not that the beherits are “different” per se, but rather they already served their purpose with their respective Apostle, which is not the case of the one Guts is carrying, not yet at least. Hence why the Skull Knight didn’t try to take it. 

I hope it makes sense, please have a nice day Anon!