Tyx
Other players cannot choose or affect your Hucksters at this location with action cards if they could legally choose to affect Tyxarglenak instead.
Hanshanks
While Hamshanks is unbooted at a location you control, other players cannot choose or affect your dudes at this location with their abilities if they could legally choose to affect Hamshanks instead.
If a player controls both Huckster Hamshanks, who is unbooted in a location they control, and Tyx at the same location you create the following situation:
Both say you can’t choose X if you can choose Y legally instead. Which would make both illegal targets, which turns off both traits in regards to Action cards, as Tyx only protects against action cards.
When they go to use an ability from elsewhere, it must effect Hamshanks if able.
This does not effect abilities that can’t choose/effect either. Such as card stating choose a wanted dude, when neither are Wanted and Valeria is.
Tyx being a Huckster changes nothing. He’s still a legal choice for anything that can choose him.
Tyx Xp
While Tyxarglenak is unbooted and has a Mystical goods, he has +2 bullets and all opposing Shootout actions must choose him if possible.
You’d have to target Hamshanks here (assuming he’s unbooted, in a location you control), as you can’t choose Tyx XP. “Can’t” trumps “must if possible”.