The Space Wolves are not the current day executioners of the Emperor.
In truth the Space Wolves legion always fulfilled a role that was most needed in the society of the Imperium, during 30k and the great crusade/Horus Heresy they were the executioners, being one of the few legions before the HH that felt OK with fighting other space marines.
Many times during the HH books it has been described that Space Marines would never have even imagined fighting other Space Marines, the Wolves did not have such restraint.
As you said yourself it was heavily hinted they were the ones to deal with the lost legions but they also were the ones that actually fought with the World Eaters legion when Angron was called to a halt.
Now however they are saviors
It is well known that in current 40k compassion and a sense to do what is right is far fetched. However, not with the Space Wolves.
During the first war for Armageddon, that is the invasion of Angron with loads of daemons the Space Wolves came to help the population and together with the Grey Knights they drove them off and banished Angron.
However, due to the absolute secrecy of both daemons and the Grey Knights the world and its population was to be purged and refilled with other colonists from other worlds.
The Wolves, however, did not just fight off a daemon invasion and save the world just to let the Grey Knights purge the population after and actually engaged in a short scale (and mostly non-lethal) war against both the Grey Knights and the imperial Inquisition!
I think it speaks volumes about the current day Space Wolves that they were willing to do this, just for some civilians (I mean look at the Black Templars) and I'm willing to bet that almost no chapter save the Salamanders would have even attempted to stop the Grey Knights and save the population of Armageddon.
Also as @Nino Memelink pointed out the Minotaurs chapter are the ones currently fulfilling the role of executioners because of their eagerness to fight other Astartes and seemingly great effectiveness. Also heavily implied they are backed by a High Lord of Terra so there is that.