Normal users and sticky
 

Is there a way to give individual a user or a usergroup the possibility to set a thread as sticky without adding them to the moderator group?

No. But I suppose you could create a group from the Moderator group and rename it something else and take away all perms except 'Can Manage Threads'. However then they'll get other perms too like merge and split.

There may be a better way of doing whatever you're trying to accomplish. Having a bunch of people sticky threads would just result in so many stickies they would no longer be important.