Martial Maneuvers Are Usable Outside Combat

Tome of Battle puts no restrictions on using maneuvers outside of combat. The text does, however, put some restrictions on recovering maneuvers outside of combat. In the chapter Blade Magic in the section Recovering Expended Maneuvers under the heading End of an Encounter there's this text:

In the case of a long, drawn-out series of fights, or if an adept is out of combat entirely, assume that if a character makes no attacks of any kind, initiates no new maneuvers, and is not targeted by any enemy attacks for 1 full minute, he can recover all expended maneuvers. If a character can’t avoid attacking or being attacked for 1 minute, he can’t automatically recover his maneuvers and must use special actions to do so instead. (40)

Emphasis mine. Those special actions are described in the same section, so, for example, a warblade recovering maneuvers this way recovers maneuvers more slowly than by using his special action but still might find this way useful if prevented from making melee attacks.

Stances
As an aside, in the chapter Blade Magic in the section Initiating Stances and Maneuvers there's this text:

You can remain in a stance outside of combat situations, and you can enjoy its benefit while exploring or traveling. (38)

So this is pretty much unambiguous.

The DM's Concern
While the DM's concern is valid--it probably is easier for your character to get a better result on his Concentration skill check than it is on his normal Willpower saving throw--, abilities are supposed to do stuff. There'd be little sense in picking such a maneuver if it didn't do what it was supposed to do: give your character a better chance at making one successful Willpower saving throw, after which the maneuver must be recovered. If pressed, tell the DM your character must be targeted with effects requiring a Willpower saving throw twice in rapid succession, and the second effect will require your character to use his normal Willpower saving throw bonus. Foes will probably figure this out quickly in combat, and others will try to exploit your sometimes-weakened Willpower saving throw as your character's reputation for momentarily indomitable will grows.

Well, it depends.

If you go purely RAW, you can't.

But that is silly.

The rules of when combat starts are really a disapointment. I would suggest you to see this with your DM. Most DM's house-rule obvious silly things, like the XP-Penalty for multiclassing, so maybe your DM would go the same way with those rules.

Afterall, what sense would make if you got penalized by going first?

In this special case, I would let the sniper shoot his arrow and do his hide check. That's a valid way to rule this situation that won't really break the game.

Talk to your DM and check with him. There's no better person that address this besides him.

Want a RAW solution?

Create a diversion.

Use your surprise round to throw a rock somewhere so the enemy look to that side. Done.

Problem solved.