Fix your description. It doesn't work without any weapon.

It really annoys me that you can't use this skill if you're silenced, how does that stop you from punching someone?

One of the best go-to skills when in trouble and out of knocks and crowd control, especially in early game. Just switch out shield and bam

The thing is, it deals 80% of your base damage for 1 AP and can also backstab. Superb attack for ambidextrous rogues.

if you switch what 1H weapon you're holding in your main hand you can refresh sucker punch on the spot. this effectively means that if you always carry a few extra daggers you can lock down a single target eternally by cycling through them for fresh punches. not very practical for most combats but pretty entertaining.

I just love that skill so much.

Does anyone know which of strength or finesse this scales with?

It deals 80% of your damage for 1 AP.
Since unequipping your offhand reduces your damage by one third (offhand weapons only deal 50%) this skill effectively deals 56% of your regular damage if you're dual wielding. (doesn't matter if you're offhanding a shield or nothing anyway.)
If you spend an AP to equip your offhand again, to deal more damage again, sucker punch is effectively on par with battering ram and battlestomp damage and cost-wise, except it does not have a cooldown for as long as you equip and take off your offhand, or swap your mainhand with another 1 hand weapon while your offhand is free.

In case you're following an ambidextrous playstyle, I highly recommend carrying a shield into a fight and unequipping it when you want to profit off your Single-Handed combat ability, Ambidextrous or Sucker Punch, since taking off a shield doesn't cost any AP at all and it essentially gives you the shields tank stats for free.