Lol no it's not illegal. It's a hat. that string is on all those kinds of hats. The reason for not being able to have two designs in one is so that it's not worth more by giving the buyer 2 in 1. This design would look weird without the string and the string definitely could not be sold by itself so there is no reason this would be illegal.
All plusses are appreciated and here are some other designs you might want to plus too!
https://tengaged.com/design/id-264887/designer-glasses
https://tengaged.com/design/id-264886/glossy-lips
https://tengaged.com/design/id-264888/safari-hat <== You are here.
Thanks again!