This isn't only an Aspie issue - maybe that will help you feel less shame or guilt about it (if you do). Sex therapists (haven't been to one but have seen them on daytime talk shows Lol) always say to touch without other expectations. To touch without it ever leading to 'more'. Only that way can both parties relax, and enjoy the actual moment they are in.
As for other things to do... how about if he draws a bubble bath for you? Do you like the touch of water or is it any touch.
You can write little notes and leave them where the other will find them. They can be romantic or silly. The thing is you know the other one is thinking of you. It may not seem a big thing but we used to do that (more factually, I did, Lol) and I know it was missed later when that stopped.
If you like food or wine you can give each other those types of gifts now and then. Same with flowers, or a video game or whatever might make the other one smile. It doesn't have to be typical romantic stuff like you'd see on a Hallmark card.
How about going on a helicopter ride (if you both like heights) or some small weekend trip... do things together, whatever your common interests are. It's hard to say more without knowing more about either one of you though...
But certainly there are many romantic things which don't require touch. The sense of smell is another. Candles, lotions. Do you enjoy beautiful things? Bring each other home something pretty to look at... a painting, anything. Also, maybe if you both took massage lessons... and so you knew what exactly to expect every time... you could eventually learn to give each other massages, and even come to enjoy some type of touch. Massages generally follow a specific pattern. Good luck. My advice feels kind of clunky but maybe some of it will inspire your own idea.