you could buy any mittnes you liked and just add the string yourself. I put elastic on mine and then cut the elastic just big enough so that it comes about an inch below my cuff, maybe less actually, maybe 1/4 of an inch. That way when I take my mitts off, they are not flapping around. I can wear them and the elastic stops them slipping down and that constant pulling them back up thing.
You could also make a string with a crochet hook and a matching yarn. Just do a slip stich and one chain repeatedly until you get a string. Sew onto mitts, or attach press studs or something if you wanted quick release mitts.
Good luck