Furthermore, what to say instead of let me know if you need anything?
What to say instead of “Let me know if you have any questions”
- “Please let me know if you have any questions.”
- “If you have any other problems, just let me know.”
- “If there is anything else you need, please let me know.”
Secondly, do let me know vs let me know? If you say Do let me know, you are making your request more emphatic and suggesting that you really mean what you are saying. It can mean don't hesitate to tell me. Please let me know can sound more routine and automatic. Please do let me know sounds like "overkill" and I would be surprised to hear it.
Considering this, should you have any queries meaning?
Should you (= if you) ever need anything, please don't hesitate to contact me. The example talks exactly the same of your concern. So, both the sentences are correct and say the same thing.
Is saying let me know rude?
Just let us know.
I agree that it's not a bad thing to say, but its suitability depends on the context. Confirming that you are ready to fulfill an offer is one thing. Making a request of one's boss is something else entirely. It fits your context, but I think it's a bit too blunt for the context of the OP.
