So I don't know a lot about CNC and my personal habits regards dust collection definitely leave more than a little to be desired. But I'm concerned primarily that the shop vac won't have enough oomph to pull sufficient amounts of dust away.
The (relatively..) short version is that shop vacuums have very different characteristics from dust collectors. The shop vac is a high pressure low volume device. This makes it quite good at removing small amounts of fine dust within a confined area (more pressure == more speed so better at pulling small bits but not a lot of air volume). On the other hand it doesn't have enough airflow to really remove large volumes of material. The Dust Collectors on the other hand are low pressure high volume systems that can move a lot of material but sometimes falls down a bit on removing fine dust really close to the source for fine stuff. So in my case I use the shop vac when I'm running the router (the festool 1010 has a pretty decent pickup shroud that goes around the blade), and that keeps that remarkably clean (unsure on allergy dust rates..) But I don't do a LOT of router work, if I did I think I'd have to rethink how I did things because the container on the shop vac wouldn't likely keep up very well. OTOH for things like the planer the DC is the only way to go because of the huge chip volume. Where it gets tricky is with things like the tablesaw, mine only has under-blade collection with the DC so even when it's on the fine stuff on top tends to fly around, in an ideal world I'd have higher pressure but lower volume (aka a shop vac like thing) collecting on top to pick up the fine spray. The CNC has a bit larger "collection" area than a router though and you can easily shroud it so the airflow is all pulling in nicely.. And a DC's ability to move a large volume of air can remedy a lot of sins so if you have well designed pickups Like Darren mentions that seems like the way to go here.
The other consideration is disposal of the dust once collected. My DC is a modified HF with a Wynn Filter and Thien Baffle over a pre-separator drum setup. The Thien Baffle does a pretty decent job of keeping the chunks out of the filter, which is important because once the filter gets clogged it's messy to clean and the performance drops precipitously. My main issues with this setup have been: keeping the seals all good (especially around the filter), and dumping/cleaning the thing when it gets full/clogged. For the first part of sealing I've had some luck with judicious application of rubber door seals where leaks are noted. Part of the issue with sealing is that the HF unit is a bent tin can (so to speak), so getting the filters to seal was doable but required a bit of work. The other part of sealing is that my collection bin was a "free if you take two" plastic drum which is not round, flat, nor regular in any way. I addressed the drum as best as I could with a straight edge and a rasp/file but its still been a bit of a challenge. For dumping, it's kind of a mess. I'm going straight into the drum and so I have to dump the drum which .. can be a lot of dust. If I had problems in this regards I'd be seriously looking at some way to put it straight into a bag more effectively (and should anyway). The other problem is that when the filter itself gets clogged it can be a bit of a mess to clean it out. My best shot there is to use a vacuum to suck the dust out of the pleats but that's sort of slow and still has a fair bit of exposure. "Better" systems have somewhat automatic filter cleaning (ideally by reversing the airflow across the filters to blow them clean) without having to open the thing up. That would be super nice, but you're getting into $$ there.
Given your situation and setup I think your best bet is probably a DC with a setup akin to how Darren describes, but put it outside the shop and away from where you'll be directly exposed to dust that escapes if the filter, bin/bag, etc.. aren't fastened perfectly. I think you can get away with the outside-of-the-shop DC because of your lovely weather
I think I'd forgo the drum based baffle because of the problems I've had with getting it to seal well and the issue of dumping after. The Jet knock off of the Thien Baffle - their "Vortex Cone" - or a Thien Baffe in the ring of the DC (
https://woodgears.ca/reader/jensen/index.html and
http://www.jpthien.com/smf/index.php?topic=29.0 for examples) so you can just take the bag off and dump it directly without moving the stuff around more would be my suggestion. This is assuming you don't want to spring $$$ on a larger cyclone type system.
One side note on the Thien Baffle, the separation is directly proportional to the narrowness of the slot. The narrower the slot the better. I had originally tuned mine for the tablesaw and it worked beautifully even for the drum sander. Once I got the planer the larger shavings clogged it up pretty badly though because the slot was to narrow. Widening out the slot made it work for the planer, but let more fines get into the filter from the TS and sander (there ain't no free lunch). I think the CNC would likely put our pretty small chips so you can probably get by with a narrower slot, say maybe 1/4" or 1/2" at most. I'd probably start at 1/4" if you're planning on making one.. and then make it so you can easily take it out and make it wider if you have clogs, kind of sneak up on the thing.