There is absolutely nothing wrong with riding a horse on a loose rein with one hand if he's in a snaffle. I ride all my greenies that way eventually when I'm working on their neck reining. I only ever pick up with both hands when I need to correct something that they're doing.
How I have the best results transitioning a horse up from the snaffle to a curb is I wait until the end of a ride when they are relatively tired and less likely to act up. I put them in the curb and take them to an area that they are very familiar with and comfortable in. I start on the ground, applying light pressure to the rein asking for bend to each side. Stay patient because they may take a couple of minutes before they can figure out the new pressures enough to give the correct way. When they do bend the way you want, release all pressure.
Work that on both sides for a few minutes before you even get on. Then, when you step into the saddle, work in small-ish circles each way at a walk, then at a trot, and finally at a lope.
Take your time and give him a chance to get accustomed to all the new pressure points and you shouldn't have a problem at all.
It's just a personal preference, but I really like the bits with the rein rings at the ends of the mouth like this
It doesn't happen often, but I have had it happen where a horse just couldn't seem to understand the new pressure no matter how patient I was. So, I put 2 sets of reins on that bit and use the rings by the mouth for the snaffle pressure that he was used to and I gradually introduced the curb pressure by slowly shortening the reins on the lower rings.
Unfortunately, I can't seem to find a bit with a mouth like the one you posted that has those rings
. I've looked everywhere and just about decided the only option is a custom bit that will be expensive as heck.