I don't think it's the "hesitate" part that makes it sound so formal, but rather the "require further information" part that does. Some alternatives that sound maybe a bit more personal would be:
"Please don't hesitate to contact/call me with any questions or concerns."
"Please feel free to contact/call me for anything else you need."
"You're welcome to contact/call me if you need any (other/further) information."
Any combination of these would make a good alternative if you really want to change your sentence. The ending phrase "with any questions or concerns" would be my choice for something you would hear frequently and that keeps a professional but warm tone.
(not a teacher, just a language lover)
Student or Learner