While not explicitly spelled out, it's generally accepted that Sneak Attack Damage is part of your Weapon Damage, the same way your Stat bonus to damage is part of your weapon damage.
It is treated as being the same Type of damage as the weapon you are using deals, and it benefits from all of the other things that impact damage.
Based on that, yes...a Sneak Attack done with a Sword of Wounding (assuming said sword was a Finesse weapon) would apply the Sword of Wounding's effects to the entire damage stack.
This is further supported by developer commentary. This is from Mike Mearls, so it is not authoritative, as if it came from the Sage Advice Compendium, but it does still represent designer intent.
Q: If sneak attack is used, are sneak damage dice part of the weapon damage dice? are sneak dice maximzd with sharpness sword?
A: i'd say yes
