I've just started using WebStorm and was wondering if there is an easy way of porting the IntelliJ shortcuts I use in VS2015 into WebStorm, instead of remapping.
Nope, as of there is no provision of exporting your Visual Studio shortcuts into IntelliJ. But yeah, you can configure your Keyboard shortcuts for WebStorm in IntelliJ.
Reference: https://www.jetbrains.com/help/webstorm/2016.3/configuring-keyboard-shortcuts.html