Would it be possible for a spaceship to fly through space with the propellant stored off-ship through a wormhole? The propellant-tender end of the wormhole wouldn't need to move, so the ship-end should be far lighter than the propellant that can be used. There would also be the advantage that the tender could be refilled regardless of where the ship is. It seems like this would keep physics intact, but still allow for a ship to fly with more propellant than it could carry. Is this possible, and would it work as I have described?
Not as we understand wormholes, first, you are making the mistake of assuming that wormholes are some kind of physical, movable object. This they are not, Wormholes are simply compact regions of spacetime, particularly one whose boundary is topologically trivial, but whose interior is simply connected. It is not that simply to just "move" this along with a ship. This has various issues in the manner in which they work, and even not counting all of this, the mass of the wormhole itself makes it hard to move, and far surpass the weight of the fuel.
There is also the fact that in a traversable wormhole you would be faced with a strong repulsive force on the ship-end. You would have to find a way to deal with this, without completely getting rid of this force. As this force is required for the fuel to leave it.
Also, if I do understand it all correctly, it would mess too much with the connective "pipe" between the two ends if one keeps moving. This would likely mess with the information passing through the wormhole while it is moving. Though I am not a professional in the field of wormholes, so take this with a grain of salt. It is just that the formula and resultant effects would undergo various changes with changing coordinates as I understand it.
Ellis Drainholes should be most relevant to this use, https://en.wikipedia.org/wiki/Ellis_drainhole
You can read an overview here