You can use a resistor but not a diode, how does that make sense? You really need to prevent that current from flowing, can you use a 100k resistor?
Despite what makers say you can actually recharge (a few times) alkaline cells, but their chemistry isn't stable under those conditions, so you get very few charge/discharge cycles and the capacity diminishes fast.
I don't have the hard fact to back it up but I'm going to guess that 3.6ma over a AA battery for any length of time would be very bad for the cell.
The one thing you don't mention is how often and for what length of time that voltage will be present, which is VERY important to answering your question.