On Wormholes and Paradoxes

Physics question about FTL travel/wormholes (reframing to a real life experiment that could be accomplished):

Two points in space are one meter apart. Additionally, there is another path, through a number of reflecting crystals (let's assume these crystals do not slow down light, just for thought experiment's sake) that requires the passing light to cross 1 light hour of space.

Is it possible to cause paradoxes using this set up? I am unfamiliar with all the related experiments in this area. It just seems to me that anything communicated or learned through the long path could be easily and instantly communicated through the short path without a paradox occurring.

If not, then why would here to Alpha Centauri (long path) connected by a wormhole (short path) be any different?

To expand on this point:
Positions at relative rest with each other would have a consistent measurement of universal time. Positions moving relatively with each other would not, but could calculate how far off they would be by using relativity equations. There is a big difference between traveling near or faster than the speed of light and teleporting, for this reason.

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