How can I manage and deploy snap packages without using the official Snap store from Canonical?
You can't and it's not a priority for the snappy team to support this feature. See the extensive discussion here (I'd suggest liking comments on this thread that you agree with).
On the forum I do read about 'branded stores' but, as I understand it, these are kinda subsets of the snappy store? Sorry I can't substantiate this comment better, but the feature you're asking for is simply not supported.