The solution is to increase (or decrease) the sample rate of the source to achieve the required playback speed (and corresponding pitch change), and then pass that signal through a sample rate converter to produce an output at the appropriate fixed sample rate.
This is a relatively simple thing to do these days, and shouldn't result in any unwanted artefacts at all, given a half decent src algorithm. Most DAWs have some kind of speed-change functionality built in that integrates these functions.
The trouble starts when you want to speed something up, but also maintain the pitch... and that almost always sounds nasty because of the frantic signal editing that is required! Happily, you don't need to go there.
Technical Editor, Sound On Sound