If you can sew at all or know someone who can go to a cheap thrift store get a pair of mens jeans about a size 36 or smaller (measure srm of chair 1st) you want the waist of jeams to fit on arm of chair without sagging as then it would be easy for it to gap open.
Cut the jeans off just below pockets turn wrong side out stich up the bottom this can even be done by hand if no sewing machine but sew it a couple times you want it fairly strong. With the pant legs cut off some strips about 4 inches wide no longer than 10 inches long easire to shorten than to make longer tho, sew those in half lengthwise then 1 end to front or back of jeans Just like handles on store bought purse. the other end velcro so you can hang on arm of wheelchair. This gives the person actually using chair a bag they can reach easy with a few pockets as well.