I think OP's no wipe leads to a messy pour next time, as it just adds to the residual gloop that builds up at the opening each time.
Ms. OP's finger, no offense, is probably dirty, but the sugar and/or vinegar in the sauce, plus the dehumidification from the fridge should take care of that also.
Consider how long people leave condiments in the fridge under all sorts of circumstances and we're not living in fear of old ketchup and mustard. If it's an issue, a compromise of wiping it with a little piece of paper towel should resolve it for you guys.