Can I change the default music player app on my iPhone? If so, how?

I want to change the default music app on my iPhone from Music to Spotify. Is this possible? My first guess is that I would have to jailbreak my phone. Is there anyway to do it without jailbreaking?

Uninstall the default music app in iOS 11. Restart. voila.

My headphone control now works with wynk music app. control center also shows wynk music.

I would say there isn't really any default music player on the iPhone. You could say that Apple's Music-app is the one that opens when you press "Play" on the lock-screen or the "multitasking bar", but there's no real advantage in that.

To answer your question, no. You are pretty much unable to change any default things in the non-jailbroken version of iOS.

With that said, you can do some tweaks having jailbroken your device. If you would like to use Siri to play your Spotify music, there is a jailbreak app for that called AssistantLove.
Other than that, you could use the jailbreak app SpotiPlay. It makes the Spotify-application the one used on the multitasking bar.

There is no way to do this on a non-jailbroken iPhone. And even after jailbreaking, there is currently no tweak which lets you do this.