Cold crashing in bucket with 1 gallon of headspace

I'll be cold crashing my IPA soon and I started thinking about how this time around I was planning on cold crashing in the primary bucket instead of first transfer it to a carboy for a few days and then put a solid bung on it.

Since it's a bucket, I don't have a solid bung. Would it makes sense to use my normal 3-piece air-lock with sanitized saran wrap on the bottom of it? I'd like to prevent suck-back, but I am a bit worried the amount of pressure this will create being in a bucket with 1 gallon of headspace.

Sorry to revive such an old thread, however I have not been able to find anything definitive about cold crashing in a primary fermentation bucket.

Searching these forums I've learned the following:

1. The CO2 blanket is a myth for protection from oxidation during cold crashing.
2. The S type airlock will (potentially) prevent the liquid from being sucked back during the cold crash.

The fermentation bucket is not nearly as airtight as a carboy and the head space is much greater. Does this mean that oxidation during a cold crash is potentially more problematic in a bucket compared to a carboy? I've also read to not worry about the oxidation since it is negligible compared to other steps in the process (e.g., transferring to a keg or bottling bucket). Is this a concern when cold crashing in a bucket?