The day counter is not too bad, but you also get the commentary from the guards.
It annoys me for some reason, though I guess I can always join up with the companions and refuse the lycantrophy thing. But I know myself too well, eventually I would just go for it and cure it after the questline.
The reason that I don't want to be a werewolf is purely because I want my Nord warrior to go to Sovngarde. So yeah, does the commentary from the guards and the day counter bother you too? I really wish I wouldn't get so focused about such a little issue.