Well, what are planted around them again? If they're tomatoes, you may be able to prune the lower leaves and suckers and let the squash grow underneath, if they're bush beans, they might possibly be done before the squash gets there and might be removed, etc. If what you have is lawn beyond the edge of the bed, you might let the squash escape out into the grass. (Vertical trellis is not possible -- yes I would take it out so it doesn't crumple up the leaves as they grow, but I've heard of setting up an angled/ramp trellis out of stiff wire material like concrete reinforcing wire and hogwire fence. Squash will start growing tendrils after they're bout a foot long and *can* grab on.)
I would pick one to stay and let it grow from the current location. You can "train" them by gently shifting the leaves, using sticks or bamboo stakes pushed into the ground to hold them in place, and by leaning the vine in one way or another, direct the way it grows, though once the vines start to branch, you may run into some trouble, but let's cross that bridge later, shall we?
How big are they? Every reference says squash really doesn't like to be moved, but I suppose you won't lose anything by trying to transplant the other one with PLENTY of soil around it -- i.e. Pick the SMALLER plant to transplant. Have a hole dug for it already where it is to go, then use a big shovel not a trowel, have something like a large shallow tub on hand (I use an old plastic saucer sled for operations like this) so there's no chance of losing the root ball to accidental crumble. If you don't have one, I would line that tub with something a plastic garbage bag so you can easily lift out the rootball. Fill the hole half way with water, then slide that baby into the hole.