Existence of a Technic 1M Half Beam
If I understand your question, you are seeking a spacer that can spin freely on a Technic axle. Essentially, you want a 1/2 bush that has a round hole rather than an axle hole. I don't believe that this piece exists in Technic.

The old Technic Hub/Handle (424) may do what you want, but it is thicker than a 1/2 bush:



Failing that, a minifig ring may work for what you need if you have one handy:



Feel free to post pictures of your WIP and we may be able to provide better suggestions if those don't work.

Edit:

Now that you've posted a photo, I wonder if a 1/2 Bush might just work:



Edit2:

I've now had a chance to play around with some alternate designs, and the one that I like best simply replaces the 2x2 plate and 2x2 tile with this wheel hub (3482):



This is solid and has a nice feel in the hand. It gives you the flexibility to have this rotate as tightly or loosely as you'd like.

Some others like to just use an additional 2x2 round plate: