good topic man... As nascar mike says i use a towel this is very comfortable for me... The disc thing is also another comfort for me. I think it is because my other hand just isn't hanging around there ya know? Caution i will say is that you thinking about it and pondering about it might make this JUJU a bad JUJU as it gets into your head... probably me just saying this will bring it to life. So i will say i am sorry in advance and say good luck and keep putting.
When I practice I putt with two discs and a towel, so in a tournament I walk up to each putt with two discs and a towel in hand, decide which disc to putt with as I am setting up, then my opposite hand holds a disc and a towel. This is my normal pattern, in practice, in tournament rounds or in the world championships.
The added advantage of this approach is that when I set up to putt I always have the choice of using my straight Rattler or my more overstable Magnet. Before adopting this strategy I would walk up to putt with one disc (like most people) . If either the wind conditions changed or I just re-thought my choice of putters then I would have to go back to the bag, get a different disc and set up once again. Being lazy, sometimes even if I thought I should change the putter I didn't, then if I missed I ended up playing head games on myself. Never work yourself if you can avoid it. It is your opponents job to work you. Don't do their job for them. :)
If it makes you feel at ease then do it. For me my free hand has to be behind my back. Because I THINK it will keep my release on a straighter line. It's all in the head! and yes. play as you practice.
it's all about having your mind in the right place and feeling confident in your putt. hell i always give my putter a little kiss for luck. i started doing that to knock my stress down and focus on the disc and the chains.... yes, i get a lot of reactions after but it's just what i do.