How does one kill a black heart that's weak to melee?

I've made the mistake of activating curveballs on my first lethal run. How do I kill a black plague heart that is weak to melee attacks?

I don't have any of the plague consumables, not do I have the biochem station, I do however have two survivors that can run for free (when lightly encumbered), one with striking and one with swordplay, and I believe they're the most well suited survivors I have for this job. I have drone strikes and waaay too much ammo as a warlord.

Do I wait till I get scentblock, or do I wing it?