When I design websites. many time I try make the select drop-down more attractive.
example
By default select drop-down looks slightly different in almost each Desktop and Mobile browser
but behavior on focus is different on Mobile and Desktop browsers.
My questions is
For better UX and Accessibility Is it good to leave Select dropdown with default style and behavior or giving different styling with help of JavaScript is OK?
Edit: Added after @Roger Attrill answer
I'm making a Web Application which will run on all possible devices. Mobile, Tablets, Desktops, Laptops. and both touch based and mouse based screens.
I seen one cons and that is the adding a JavaScript to make the custom design for dropdown. if we want consistent design in all devices. Because custom styling of Dropdown is not possible with pure CSS.