So long as you are force carbonating this beer, aka c02, you should have no issues racking into a keg and then chilling. Most of the problems only arise when you are bottling or warm conditioning a beer - such as racking the beer into a bottling bucket, adding sugar, and then putting into bottles. All that oxygen is going to restart a fermentation at warm temps.
I like to cold crash in primary before I keg, both to get the beer as clear as possible and to set the malt profile. Once the beer gets into the keg at a cold temp, I've never had it drop gravity points. Also, s-04 isn't known to restart fermentation, like 1968/002 and some of the other highly flocculant yeasts.
Lastly, your recipe looks fine, (gravity is on the low end) though I would probably drop the oat malt for the sugar or brewers invert. So long as you're using a quality MO, you'll have plenty of malt character. Be sure to keep your ferment temps below 68F with s-04. Once that stuff gets around 70F you'll get some nasty esters. Good luck!