Who are these wise friends? The Royal Bridge partners? Their usual dinner parry guests? Their roommates from college?
It’s interesting to have these people we’ve never met or heard referenced before turn up at this point in the play. Because he begins with “Come, Gertrude…” it seems as though he may be referring to their mutual friends – their couple friends – but, of course, he could also mean HIS friends, the Royal “Our friends” which would be the more political group of “friends” I imagine. This might make more sense given that Claudius’ chief concern about this murder are its political repercussions.