It's clear from both of Darth Sidious's canonical lightsabers that he's married to a particular aesthetic - An aesthetic that appears refined, developed and opulent. All things have humbler beginnings, and while young Sheev was whirling his first Shii Cho maneuvers, perhaps something more akin to this less glamorous design was the weapon he was granted.
Bearing the hallmarks of the style he adored in later life, but with none of the budget and finer detail, I give you my take on what Sith Apprentice Sidious's lightsaber might have looked like.
Shoutout to Brian Karasek for inadvertently giving me the idea. This is for you and all the folks at the Sith Library & Archives!
Sheev Palpatine - Sith Apprentice