For the Show Off mechanic, can I use my chosen champion (still in the champion zone, not on board) to get the Show Off benefit?

Radiance rules aren't published yet. This uses the printed card and current rules only, and it isn't a ruling on the new mechanics.

No — a Chosen Champion still sitting in the Champion Zone can't be used to satisfy Show Off.

Show Off is shorthand for "As you play [this], you may reveal [Object] from your hand and/or pick [Object] from among friendly game objects on the board" (Rule 832.1.c). The Champion Zone is a non-board zone (Rule 108.3), so a champion there is neither a card in your hand nor a game object on the board — it fails both halves of the Show Off requirement. You'd have to play the champion to your Base or a battlefield you control first, then it can be picked for a later Show Off.

One timing note: the choice to Show Off is locked in during finalization (Rule 832.1.c.2), so you can't pick the champion and then play it in reaction to make the pick legal. This matches the existing FAQ on Primordial Roar (#12841). This is my interpretation based on Rule 832.1.c and the non-board status of the Champion Zone.