You might want to try a compression garment like SPIO. They are designed to be worn under regular clothes. They have a 90-day guarantee if it doesn't work for your child. www.spioworks.com

A compression vest might work well. OR you can find those underarm our shirts and buy it just one size smaller so it can squeeze him and he can wear it under his clothes to get the input that he needs. A mis of Lavender and cedar wood might help too, just put it behind his ears before yawl go out.

I am sure you have tried this, but is it possible to get him to a quiet place, and hold him tightly? Like you are the blanket. Then, return to the situation. Or maybe pair something more portable/smaller with the blanket when you use it at home (ie;have him carry a small squeezie toy that he also squeezes at the time he uses his blanket). Then, if he gets overwhelmed/melts down while you guys are out, you can give him the squeezie toy as a substitute while you are hugging him.
We did something similar with our son when he was younger, but we were able to create a sort of cognitive over ride, in which he almost automatically went in his coping mode when in overwhelming situations.
For the substitute toy/coping mechanisms to work while you guys are outside the home, we found that definitely helps to set up many slightly challenging situations for him at home, then practice "coping" successfully (you set up the success). Setting up lots of situations where you son might feel challenged, associated with memories of coping successfully while at home, will eventually allow use of the coping mechanisms in challenging situations outside the home.
For instance, my son was about 8 or 9, so we set up simple problems that he could solve. The big breakthrough was helping him use the words "stop and think" before reacting. So, even if he knew how to solve a problem (maybe for a little guy, it's when he drops a toy), I would say "stop and think" and then help him grab the toy. We would do lots of little challenges through the day (both with pencil and paper, and in "real life" type of situations), and repeatedly say "stop and think" before he took action to solve the problem. It took several weeks, but soon we were able to say "stop and think" if he became overwhelmed when out. Since your guy is little, you might want to pair whatever short saying you think might be calming , with a physical action he can take every time he feels overwhelmed (maybe squeezing his hands together??)that can cue his memories of past coping successes.
Phew. That was long! Hope that helps.

Look up the iPad scholarships. Always take it with you when you go out with a pair of headphones. It works wonder. If that's not an option, take his favorite jacket with you. Might be of the same use as the blanket. My son, we use breathing. Three deep inhales and exhales and then he's usually okay once I calm him down.

You can also try covering his ears, speak through the back of your hand so your muffled voce is all he can hear and talk to him or sing to him his favorite song.

Maybe try a weighted jacket? They sell them online.