Is it bad to double freeze seafood?
Refreezing food, assuming it has been treated appropriately while thawed, and not held overly long at thawed temperatures, is fine from a safety point of view.  This is as true for squid as it is for any other food.

You may have some loss of quality from the thawing and refreezing cycle.  Home freezers are not as cold and do not freeze as rapidly as some commercial freezers or blast chillers.  The ice crystals that form within the will have time to grow larger under home freezing conditions, leading to a greater loss of moisture and possibly deterioration of texture.

Since you have been doing this a while, you know how your particular squid is affected by the process.  If you find the quality in the acceptable range--and it probably is, especially if they were blast frozen aboard the ship that caught them originally--then no worries on that front.

See also:  How dangerous is it to refreeze meat that has been thawed?