Agree on what folks have posted....lots of brushing. I have two fluffs and a short haired, on all of them I use the Furminator which is one of the options available. I LOVE it! Really good at taking out undercoat which is what's being shed for the most part. A bit of advice, though, when furminator'ing do it outside!
Oooooo, bad idea getting a corgi if you wife has a problem with shedding, there is no cure for that, its a corgi trait lol. Here are some past discussions that might help you out. Good luck!
There are tons more, but these couple will hopefully have some insightful information for you. Personally, at my house we have a furminator and a really really good vaccum.
On a side note, here are a number of past discussions about shaving - not usually recommended and I don't think it would help with the shedding issue.
I just have a steel Afro-type comb, and I don't comb all that often (every month or two?). It does help when they're "blowing their coat". I do it to prevent matting, not to reduce shedding. Never tried a furminator.
We are kind of slobs, and don't vacuum often, and our house really isn't all that furry.