Although Andy Woodman is/was the current favourite, I’d say it's incredibly unlikely given the statement mentions “a change in personnel does not lead to a switch in overarching philosophy.”
None of the names really jumped out at me, the only manager in this league that I might be tempted to look at is Phil Parkinson (no not that one!), Altrincham have competed very well for a part-time team the last two years and been no-where near the relegation spots like the other promoted teams.
If I had to make a bet, it would be that the new guy won’t be on that list… I’ll go for Ian Foster, current England U19 manager. No inside knowledge, but fits what the owners would want.