I don’t know anything about The Handmaid’s Tale, sorry.
I think in order for this AU to work, you’d either have to use Lady Loki, or do a more convoluted omegaverse where only certain men can get pregnant. Though if you went that route, I could totally picture Loki as the commander and Thor as Alfred. He’d even get to wear his signature red. Cast Sif as Loki’s bitter wife and bingo…have fun!
I started writing a Thorki Handmaid’s Tale AU last year but haven’t touched it (or any fanfiction writing) in a while. But the way I framed it was that Loki was the barren “wife” because he’s actually a non-childbearing man rather than intersex, which is how people usually get Thorki arranged marriage AUs to work. Here’s where I initially posted about the idea. I might pick it up again at some point… definitely not Hiddlesworth, though.