Sage Advice now says No
With the release of the 2020 Sage Advice Compendium, this question now has a RAI (rules as intended) answer. According to Jeremy Crawford:
Can I hand a shadow blade to another PC? It only says the blade dissipates as I throw or drop it. No. The intent is the blade vanishes when you let go of it (that’s one of the meanings of the word “drop”).
Beyond Sage Advice
As a GM, I would probably disallow this tactic even without Sage Advice saying it won’t work, though. Anothe spell that is similar to shadow blade is another second level spell, flame blade. Flame blade says that “If you let go of the blade, it disappears”, which supports the idea that blades conjured with a spell are meant to be used by the caster, and only by the caster.
Compare this to the warlock’s Pact Boon option, the Pact of the Blade, which says that “Your pact weapon disappears if it is more than 5 feet away from you for 1 minute or more”. This allows another creature to use the pact weapon, and the SAC supports that by saying “ If you’re a Pact of the Blade warlock, can someone else wield your pact weapon? Yes. Someone other than the warlock can use a pact weapon before the weapon disappears”.
The fact that other blades conjured by spells disappear when the caster isn’t touching them, while not-conjured-by-a-spell blades can be separate from the creator, suggests that this spell should follow similar rules, even if it can be thrown (unlike flame blade). So as a GM, I would likely disallow this tactic even without the SAC ruling.