Shanks are the long side pieces on a bit. What you're looking for is still going to be a curb bit, but something jointed. From my understanding there's really no such thing as a snaffle with shanks. They're still curbs just with a different mouthpiece. He may respond better in a nicer curb. TT's can be all sorts of messed up confusion with communication sometimes and some horses just hate
them. My old barrel racer was ridden in one by his previous owners & would constantly grab the bit and jerk his head back and forth. When we switched bits it made a huge difference. He was more relaxed to flex at his poll and stopped his head jerking.
Does he neck rein & listen to hand/leg cues pretty well? I personally advise doing most of your schooling in a snaffle anyway then working in the curb just to "fine tune" every so often. Also remember, we can give suggestions but ultimately you need to find something YOU like and your horse is comfortable in. I'm a fan of the Myler bits: Toklat - Horse Tack - Saddle Pads - Horse Riding Apparel - Myler Bits - Bits
They are expensive, but you can find them cheaper. I'm just really a fan of the mouthpiece. I believe you can show in them for WP too.