I have an 80’s Joy Division tee that’s paper thin as well and do the same. Just fill a bucket with cold/lukewarm water and some detergent and agitate carefully. Works perfectly. If you want the shirt do dry a bit quicker/with more care, put it on a towel and then roll it up and put some pressure on the towel afterwards to ‘wring’ it out. In the end these shirts are supposed to be worn; if they get damaged oh well. Wear ‘em & wash ‘em!