This doesn't really solve my problem, since Slack is definitely one of the apps where I want my Alfred snippets to auto-expand. However, I didn't think about how Slack might have it's own expansions.
It turns out Slack doesn't, but OS X does include some by default, like "Smart quotes" and "Smart dashes". See this tweet: https://twitter.com/slackhq/status/588839335748837376
"Smart dashes" turns two dashes (--) into an en dash (–), which my arrow shortcut does include. I tried turning "Smart dashes" off, but I still get the "Create snippet" Slack dialog when I try to use my Alfred