Today, during a strike, my opponent focused a unit that featured unit damage icon and one blast damage icon. He applied the blast damage to the engaged objective, but did NOT want to apply the unit damage to the only available participating opposed unit because of the consequences of that unit being damaged.

Is this an option? Can you decide to activate one icon on a striking unit but not the other?

It is not an option. When focusing to strike, a Unit must use all of it's combat Icons available.

For further clarification and all that, I've updated this with excerpts from the Core Rules.

Under the heading Resolving a Strike on page 20

"To Resolve a strike, a player follows these steps in order.

1. He chooses one of his participating ready units.

2. He focuses the unit to strike (i.e. places a focus token on the card).

3. He resolves the striking unit's combat icons by type."

The only exception is targeted strike. If you've cleared the engagement of units the strike with Luke you do not have to use t strike. It is a you may target outside verge engagement not a you must.

Yeah, but you're still resolving the unit damage icons, and if there is an enemy unit in the engagement, you can't opt out.

Well, technically you still have to use his unit damage icons, they can just be used against the 0 units remaining in the engagement, instead of one outside the engagement.

Thanks, guys! I appreciate the help.