Have to say I haven't done it your way round - we've completed three rounds of email outreach then submitted a disavow file, so I don't want to guess to far on advisability of doing it the other way around. For starters I've no idea how well / quickly Google handles domains removed from a disavow list.
Your first assumption needs comment though - every domain we're removing links from was from a spammy website (zero quality SEO directory), as a result of a submission package they bought years back before I joined.
We managed to get about 50% of the list removed from that email outreach process. Granted one was a directory network with over 100 domains, but even counting their domains as one that we got about 40% success.
Around 10% responded with a demand for a fee - ranging from 99c to $50. Clearly all those were instant place in disavow list 
So to summarise I was really surprised how successful the email outreach part was - we'd been expecting next to nothing by way of response rate rather than around 50% success.
Even if you do it disavow first, hoping for a Penguin update in the next three weeks so the file is actioned prior to your season starting is a little optimistic!
