Scales will make your Fishy hat look more like a real fish. This is how other knitters knitted up their scales:
String or nothings's scales
Kim Salazar of 'String or nothing' knitted several hats with almost real fish scales. It's a stranded pattern over 6 sts, that fits nicely in the 90 stitches segment of the body. You can find chart for this stitch pattern on her website.
These scales are inspired by Anne Campbell's Circle Sock Pattern
Use a Multiple of 8 stitches:
Rows 1-3: Purl.
Rows 4-10: K3, slip 2 stitches purlwise with yarn at back, K3.
Rows 11-13: Purl
Rows 14-20: slip 1 stitch purlwise with yarn at back, K6, slip 1 stitch purlwise with yarn at back