First off, you can use DPP to "render" a Raw file into your chosen color space, whether you are sending to PhotoShop as a TIFF or saving as a jpeg. I don't have DPP on the (laptop) PC I'm at right now, but there is a tool to do this on and image-by-image basis, or as a batch, or in Tools I believe you can set the default working color space to whatever (sRGB, aRGB, wide gamut, etc).
A couple considerations: First, it's important to keep an image in the 16-bit rendering if you are going to do color-space "dickering" in, say, PhotoShop, because the 16-bit image will keep the "breadth" of your color/tonal info so converting the image will not be "messy" compared to an 8-bit image. This can be done with TIFF. With jpeg, you'd use 8-bits, not as good. The choice does have a "cost", though, in that a 16-bit image will have a relatively large file size which needs to be saved (the "original" file) in the process of working in PhotoShop...
Then, another consideration is that PhotoShop itself has ways of working with color spaces, some that you set as the "default" for when you bring in an image, or you can adjust things "on the fly". For example, for images destined for an aRGB process/print, you can set PhotoShop to either use the aRGB color space, or you can set it to accept and work with an aRGB image "as is" without having to convert it to aRGB. Then, of course, for those destined to be used for the Web (or email/sharing with the "public"), you may want to set Photoshop to either use sRGB as its working space and convert non-conforming images, or to ask you when it opens such an image, or else you will need to specifically convert your image when preparing to save an 8-bit sRGB jpeg.
At any rate, you set up PhotoShop specifics for this in the Image/Color Preferences dialog.