If they are sitting in water in the tray, don't do that. Any water left in the tray should be removed -- I use a turkey baster.
The cucumber seedlings are likely too big. If you can't plant them yet due to temperatures being too cold, you have started them too early. Unlike tomatoes, etc. cucumber should only be started about 2-3 weeks before planting max. By the time the leaves grow as wide as the containers, the branching roots are pushing against the side of the container. Cucurbit seedlings are sensitive root disturbance. They are also heavy feeders and need more fertilizer than others -- this compounds the problem when you start too soon.
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