To me, honestly, 挟 means ‘squeeze (between)’, especially in the verb 挟む, whose て-form is 挟んで.
My personal preference for a mnemonic would be something like ‘You have a friend called Hasa who likes setting up mousetraps around your house. Whenever you get your finger/toe stuck in one, you shout, “HASAAAAAAA!!!”’ (However, maybe this only works for me because I’m used to names like Hassan, which could also be useful for remembering the て-form.) If you want to keep the ‘husband’ while making it actually useful, you could pretend you have a problem pronouncing the letter B. In that case, husband -> hasand, which is basically the て-form.
(PS: I’m only recommending screaming, ‘HASAAAAAAA!!!’ because it’s more memorable that way. You can imagine the pain/shock/surprise due to the mousetrap if you wish, or ignore it if that’s too unpleasant.)
Possibly so. However, I have a feeling using ‘husband’ is just as difficult in this case because it sounds different from the reading we need to remember. And like I said, this mnemonic would work for me because I know people named ‘Hassan’. It might not work for someone else if they find the name hard to remember, and so it’s just meant as a suggestion.
Personally though, the reason I know the reading for this is because I’ve come across the verb several times, and I think the instance that really made it stick was a scene from Shield Hero: the heroine had just prepared some sandwiches for breakfast. (Pardon the stereotypical sandwich-making. I didn’t write the story, and thankfully it’s a lot less stereotypical otherwise. For that matter, the hero actually does the bulk of the cooking overall.) I thought I’d heard something like パンの"はさん" as she talked about ‘making it from leftovers in the castle kitchen’, which was obviously rubbish because はさん is not ‘leftovers’, but looking up the transcription and finding something about using the bread to ‘sandwich’ everything together gave me a permanent mnemonic. Every time I hear はさむ, I think about the hero and heroine having sandwiches together.