Can I play Shen as a reaction on a showdown where I am the attacker?

No, you cannot play Shen as a reaction to a showdown where you are the attacker.

According to Rule 813.3.a and multiple RiftJudge FAQs (such as FAQ #8206 and #2593), units can only be played to a battlefield you control. As the attacker in a showdown, you do not control the battlefield where the combat is taking place.

While Shen has the [Reaction] keyword, which allows him to be played during closed states, it does not override the fundamental restriction that units must be played to a location you control. Because you do not control the battlefield you are attacking, you cannot legally play Shen there.