Hi OP. Not sure if you're still looking for replies on this or if you've already made your decision. I'm in my mid 30's and was in a similar boat to you - DH had no chance of fathering a biological child. We tried a couple of rounds of ICSI with his sperm, but there was just no chance. It didn't work and the results were very, very poor. So we moved onto a donor.
What I would really recommend is, if you do go for it with a donor, skip the IUI.
I had 9 rounds of IUI with good quality donor sperm, as a healthy, fertile woman in my early/mid 30's. None were successful. The chance of IUI working each time is <10% (and even lower when you reach 40). It's like throwing a dart with a blindfold and hoping it hits, and the disappointment each month is awful.
For you, with your age and your low AMH, I think it's unlikely that IUI will work.
I am now pregnant after my very first round of IVF with donor sperm - that was what I needed.
If you can, just skip the IUI and go straight to IVF. Also, ask for PGTA testing of the embryos if you do IVF (even if you have to pay for it, if you're able to, it's worth it). It decreases the chance of miscarriage and significantly increases the chance of a healthy embryo implanting.
Also, NHS treatment is not great. Our ICSI was with the NHS and there was a stark contrast when we went private. I don't know if you can afford it but if you can, I'd recommend you go straight to IVF at a well rated, private facility.
Good luck whatever you decide.