I don't know of a way to do this natively on Spotify's web player, but I created a userscript to allow the left and right keys go to the previous and next tracks, respectively (no Ctrl or anything needed).
You can install it through GreasyFork or copy-paste it below:
// ==UserScript==
// @name Next and Previous key shortcuts for Spotify
// @description Allows the left and right keyboard arrows to be used to go to the previous and next songs on Spotify.
// @author Zach Saucier
// @namespace https://zachsaucier.com/
// @version 1.1
// @match https://open.spotify.com/*
// ==/UserScript==
(function() {
'use strict';
window.addEventListener('keydown', (event) => {
switch(event.code) {
case 'ArrowLeft':
document.querySelector('.spoticon-skip-back-16').click();
break;
case 'ArrowRight':
document.querySelector('.spoticon-skip-forward-16').click();
break;
}
}, false);
})();