You used to be able to get Lycra swim caps, I got one form a triathlon with my number on it. Possibly more comfortable that a rubber swim cap.
https://www.amazon.co.uk/s/?ie=UTF8&...l_7gmla9lgyh_e
Lifeguard traditionally wore cotton red and yellow quartered swim caps with chin ties, for competition clubs had matching swimsuits and cotton caps in club colours.
https://www.rlssdirect.co.uk/categor...+Hat+-+Cotton/