If my Ruined Rex dies and my opponent only has a single unit on board which has Deflect, can I choose to not target that unit and decline triggering Ruined Rex's Deathknell ability?

No, you can't choose to skip triggering the Deathknell or refuse to target the unit. Here's how it actually plays out:

1. Ruined Rex's Deathknell is mandatory — there's no "may" in its text, so it triggers automatically when he dies (Rule 808.1, FAQ #10066).
2. Since the opponent's unit is the only valid enemy target, you must target it when the trigger finalizes on the Chain (FAQ #10922). You can't opt out of targeting.
3. However, because the unit has Deflect, the ability incurs an additional cost of [A]. For triggered abilities only, Rule 404.2 lets you decline to pay that cost. If you do, the ability is removed from the Chain and never resolves — no damage is dealt.

So you can't avoid triggering or targeting, but you can effectively stop the effect by refusing the Deflect cost.