Q: The text on Desperate Grab reads “You may choose to discard…” Does this mean that the player may choose NOT to discard their hand and therefore NOT move their token?

…What about if it comes up via a Wormhole?

A: Yes, the language on Desperate Grab is deliberately optional, since it’s such a drastic move. You can choose not to do it. So if you drew it for a Wormhole, and didn’t want to, you’d just not do it, and the card would have no effect.