Quick question about weaning from the swaddle. Do you have to wean from the swaddle for both bedtime and nap time at the same time?

Deeper context: Little guy is 3 months/13 weeks. Caught his first cold this week, so sleep went from STTN to waking 2-4 times. My husband made the executive decision to put him to bed, arms out last night (we swaddle with an A&A muslin), as we had discussed perhaps just going cold turkey right now, since his sleep is so crappy anyway. He woke 3 times, but seemingly from frustration of stuffy nose, same as before, NOT from having his arms out.

Yesterday morning, prior to the no-swaddle night, I had asked daycare how they are putting him down for naps, and they said they put him in the Woombie I gave them, arms in. He sleeps better with arms held in, they said.

So, if we wean him from swaddling at night, do I have to alert daycare and ask them to also stop putting him in the Woombie? Or can he have different bed and nap routines - one arms free, the other constricted?

And of course this is all to add that we need to wean him from rhythm for naps, le sigh (swing at home, bouncy chair at daycare.) One thing at a time!

Opinions appreciated!