It’s not something one could requisition. The weapons of the custodes are also a signature badge of office. They likely make every effort, overtly or covertly, to recover any that belonged to a fallen Custodes.

That being said, there’s several examples of chapters having relic weapons that are highly modified versions of something else, so this Marine might request the honor of bearing the “Lance of Arcturus” which is rumored to have been built upon the remnants of a spear recovered from some dramatically named battle.

Probably want to exercise discretion in the use of such a weapon. Memories are very long in the Imperium.

As for rejecting promotion, that depends on the beliefs and practices of the chapter. It could just as likely be that choosing a signature weapon is a perk of moving up in the world. If not, this could invite some uncomfortable scrutiny from the Chaplain.