Dice Replacing Cards
There are 4 suits of 13, plus two extras (jokers). use a d12, d4 combo and you lose little. Use a d13, d4 combo, and you lose only the jokers.
The D4 reads as
The d12/d13/d14 reads as
2-10 same as shown
If you really want true duplication, use a d14 instead... and reroll results of Joker of Hearts or Spades. That gets you exact duplication of the deck. For lazy man, just Jokers of hearts and diamonds are red joker, and clubs and spades black.
The advantages: It generates the exact same spread for person 1, and no changes needed to rules.
The disadvantages: each player is drawing from a fresh deck every time, so either you sequence them, rerolling later duplicates, or accept the small increase in chances of simultaneous actions.
Deal at Home
Dealing out the initiative at home, then simply telling people what they got, can work quite well. Only the GM really needs to have the knowledge, but players like knowing where they fall in the count... but the count really isn't very useful in online play anyway.
So, just deal out the initiatives, Private Message each player with their card, then call only those steps YOU know will be needed.
Drawback is that you might need to set aside a deck for the game if you are uncomfortable sorting, shuffling a partial, and then continuing...