Although we do not use the SM Mini frequently, we have Audiomoths in use wichwhich uses the same batteries.
Batteries: We use Ansmann type 2850 NiMh rechargeable batteries with 2650 mAh. They work fine and had reasonable pricing. As well I have been using Panasonic Eneloop pro BK-3hCDE NiMH Batteries. They are great as well, in my experience.
Runtime: The website of Wildlife Acoustics states: 4 AA Alkaline: 210 hours (typical at 24kHz mono) --> The Alkalines have a bigger capacity / longer runtime, but that would easily be above your stated requirements, if I'm not mistaken.
Hope this helps.