Even with 1sat/B, your transaction would not even be relayed by most of the nodes, what do you try to achieve ?
Not true, in the last 6 months I did nearly all my transactions at 1sat/B and they usually confirm in about 1 hour or less.
What you should NOT do is use zero, that won't move at all. I remember some people on IRC saying its possible to use half satoshi per byte or so tho. But if you use "twice" of that (ie. 2sat/B) it often gets processed by the next block! (10 mins); or sometimes by 2~4 blocks, but you get the idea...
Electrum allows the "replace by fee" option in case you get desperate and something gets stuck for weeks, probably other wallets allow this too. It lets you increase the tx fee to an already broadcasted transaction, so you can spend some more satoshis to speed it up yourself.