I actually called the place we bought our kit from to ask about this, and they didn't know. I think there's so little data on this process, as you're finding.
We got pregnant one of the cycles using the kit even though we insemmed way before O. I want to say it was at least three days prior. We were travelling and needed to keep doing IUI to qualify for IVF (insurance thing), so we did it anyway. I would consider it very poor timing for the only insem of a cycle, but it worked. That makes me think the swimmers have close to, if not the same 3-5 day lifespan as fresh sperm. But, that could differ by donor. Not sure. If you're able to do two shipments or trust the refrigeration process and can do two insems with a day in between, then you're probably in a pretty good place.
PS -- Have you investigated getting your donor to bank as a directed donor? That might be a good alternate/back up plan.
Mommy to an amazing 8 year old, wife to an inspiring principal, and welcoming Wylie Grace! Our July 4th babe!