Mylar won't stop RF from getting through, so any product using mylar probably won't work. You'll need something with metal.
I'd suggest going to the hardware store and getting some sticky backed foil tape from the plumbing department. Not what we commonly know as duct tape, but it's used to seal and join ductwork. It comes in various widths up to 4 inches wide or so.
You could cut it just slightly smaller than your lining fabric and stick it to the wrong side of the fabric with the foil side facing out. Sew your lining in and you'll have a foil lined purse. You'll want it smaller because you won't want to sew through the foil itself, the adhesive will mess up your needle in no time.