When I recently committed to putting some of my hoarded stickers on my laptop, I got friends to place the first few, because I knew I would be paralysed with indecision.

Maybe you could use a similar mechanism of breaking the decision paralysis? If you have kids (plural), if one kid gives you a sticker, you could get another kid to suggest where to put it. If you're feeling really wild, you could give the sticker to a kid and ask them to stick it somewhere (if they're old enough to understand what kind of place would be bad/damaging)

I sympathise with not wanting to use up the stickers, but if you do use some of them, then as well as having this delightful stash, you'll also have a few cute reminders of your family scattered about. And if you fear your supply is running low, you can give your kids a standing order of "if you see any stickers that make you think of me, I want 'em". It'd make you easy to buy souvenirs for, for sure.