Can one use velcro on Shabbos?
Yes, the poskim permit the use of velcro on Shabbos.
The reason for this is that although velcro involves the bonding of two pieces, and might therefore be though to constitute tofer (sewing), the basic nature of velcro is that it is made to open and close the whole time, and the bond is therefore transient by its very essence.
On account of this rationale, Rav Shlomo Zalman Auerbach zt”l (and others) ruled that there is no prohibition on the use of velcro, even if a person intends to seal something (by velcro) for an extended period (such as a belt for a Sefer Torah that will only be opened in a week’s time).
See Shemiras Shabbos Kehilchasa 15:78.