Then be honest in the autoresponder, and specific. People are far more accepting than you expect, and vagueness is what annoys them.
What works:
Say you are away and give a date. Not away from the office, away until the fourteenth. A date lets people decide whether to wait.
Say who you are. A one-person business saying so gets enormous latitude. Customers understand a person taking a holiday and do not understand a company being unavailable.
Link the three most common answers directly in the autoresponder. A meaningful share of people solve their own problem right there and never send a second email.
Give an escape route for genuine emergencies - a phrase they can put in the subject line that you actually check for. Almost nobody abuses this. The people who use it are usually right.
What does not work: promising to reply to everything on your return, then not. If you know you will only get to half of it, do not promise all of it.
One thing worth doing that costs nothing: email your customers before you go, briefly. People who know in advance mostly do not write, and the ones who need something write early while you are still there.