[...] Let me know if you think this would snag the right (calibre) of person?[...]
Having had the insight of being a designer on the receiving end of CV submissions, in my experience I think you'll have to put up with some frustration in your quest to find someone equally apt for both media types.
Not that there's anything particularly wrong with your advert's wording - it's just that it's a hell of a lot like nearly all designer job adverts out there. It's not that remarkable... and that's the type of designer it'll most attract.
Anyone can go through the checklist of Adobe products/obvious requirements and justify to themselves that they can rightfully tick those boxes.
The place where I used to work - an online marketing agency with a small team of in-house designers [read: "you'll have to do web, print and even the signs on the doors"] - put an advert very much like this up about a year ago.
Applications came in from: the newly-graduated; the desparate for salary; the deluded; the desperate to relocate [including a subcategory: the desperate to escape their subcontinent

]; the grizzled ex-printshop veterans ["10 years experience of Quark and a permanently depressed air"].
Some were pretty good at one discipline. One or two showed what I would consider the fruit of decent graphic design education, and could just about get by doing web design by using Dreamweaver [and Flash.
Always Flash...].
Not one had what
I considered very good skill/passion/experience in both disciplines. No-one fanatical to the point of OCD about clean markup and user interfaces, whilst also able to argue the case for their five favoured print fonts. Lots of applicants thinking that design is just about 'sitting in front of Photoshop all day - and getting paid for it LOL'. Erm, no.
If it were me advertising for an all-rounder:
- I'd be more conversational in tone when writing the advert. I'd be as human as possible, to gain the trust of experienced designers who've already had their tablets burnt at the hands of larger, more corporate agencies.
- I'd drop in some names of industry-respected figures ["We're after the sort of designers that are reading Zeldman and Rutledge's blogs when everyone else is on Facebook"] to catch the eye of those who keep up to date with the latest web design machinations.
- I'd tell/warn them that they'd be expected to bring in an example of a design from the real world that they think is inspirational, and expect them to talk passionately about why they think it's so good... to the point where you almost have to tell them to shut up about it.
- That's on top of being able to demonstrate that they can hand-code elegant markup. That'd be a given.
But that's just me, and the sort of designer I'd be looking for to help
my business grow to the next level [whatever that is].
On top of advertising on our site, which of the many job sites do you thing would yield the best results?
I presume that there must be a Cannocky equivalent of Orchard Recruitment, who specialise in design/media jobs in North-west and Yorkshire. Those specialist agencies would be the first place I'd investigate.
Sure, you'll have to pay fees, but they'll save you time by filtering out the chaff and get you someone you'll be happy to pay tens of thousands a year to

.
EDIT: After all that pessimism, I ought to point out that there are plenty of good designers out there, so who knows! Good luck with your search
