Can I try to trip with the Maneuvers (Strikes) of a Crusader?
Yes, but in most cases it would be wasteful.
The tripping rules specify that
You can try to trip an opponent as an unarmed melee attack.
Various weapons amend this rule, allowing you to try to trip an opponent as an armed melee attack, so long as the armament is that weapon.
Anyway, since you can try to trip as any appropriately-armed melee attack, and most strikes allow you to make an attack, you can replace that attack with a trip attempt.
Doing so, however, is usually pointless: since the trip attempt does not result in a damage roll, any bonus damage on the strike is lost. Even if you have Improved Trip, which allows you to attack after tripping someone, that is a separate attack and would not benefit from any of the special properties of the strike.
But there are a few strikes that you can still benefit from while tripping. For example, the benefit of crusader’s strike is that you heal someone while attacking: if you replace your attack with a trip attempt, you would still get the healing, and lose nothing in the trade.