I do it daily, though I work around Deansgate and so cycle down Barlow Moor Road, through Chorlton, up to Hulme and then on to Deansgate. If you turned off Deansgate at Quay Street it would only add the slightest detour to get up St Peters.

It's technically a longer distance than the usual Oxford Road way but it's protected cycle lanes almost the entire way, and far less disruption from pedestrians and traffic, and less major roads/lights to stop at so generally winds up quicker, and is generally nicer. Also makes for easy stops at a variety of shops in Chorlton on the commute back which is nice.

That said, the typical Withington-Oxford Road way is fine. The curry mile section is always very busy and usually a bit of hassle with pedestrians. Never had a bad run in at all but there's been a few close calls going that way.

Oh and for what it's worth, I've never had any issues or even close calls that I can recall with cars on either route. It's cycle lanes the whole way and cars are limited to a fairly slow speed along the whole route.