If you want to do it you have to go cold turkey. Just like other countries have done. Stop printing $1 bills, start issuing $1 coins. Done.
In the 20th Century in Canada we ditched $0.25, $1 and $2 notes in favour of coins, and ditched $1000 notes entirely. The last series of 25 cent notes were dated 1923, withdrawn by the Bank of Canada with the 1935 series, BTW.