1 sat/B is very, very small fee
Two days ago I sent 25 sat/B tx and it took almost 2 days to confirm.
But mempool is quite small at the moment (comparing to last few days) 20k unconfirmed txs is not so much so I think your tx could be eventually confirmed, but it will take days (3-4).
I doubt you can speed the transaction with accelerators ( due to very small fee), but if you had sent tx as replaceable you can raise to fee.
It can either take a whole week to get confirmed or maybe someone can see your post and manually insert your tx in the next block. A fee of 1.002 sat/byte will usually stay way at the bottom of the "queue" to get confirmed. Mainly because Bitcoinfees.21.co is recommending a fee of at least 420 sat/byte for a high priority transaction - 420x your fee.
I would say that there is a risk of your transaction never getting confirmed. But last time I said that for someone sending a fee of 5 sat/byte, the transaction got confirmed 2 days later. So, it's really unpredictable.
Thanks for the info, Im not in a huge rush for it, I will give it a week and see what happens.