If you do not want to use GOT2B Glue or adhesive glue then gentle doubled sided wig tape if the alternative for you!
Measured at 0.8mm/ or 0.5cm this is very discreet but don't be fooled it still as strong as its big brothers.
Cut small even pieces of tape and place along the inner hairline of the cap. When your ready to install peel off and firmly press down one bit at a time.
Be Your Own Kind Of Beautiful