This is a good question, and depends on how you're running your league. If you're using a website or stat service to do your bookkeeping for you, I'd simply stick with whatever positions they assign these players. This'll save you work and is equally fair toward all players, and you usually won't sacrifice much accuracy.
If you don't have this kind of default setting to fall back on, I'd choose one source (either by vote or commissioner's decision) and abide by it. I'd recommend the following site: http://www.baseballamerica.com/today/Stats/playerfind.html
Just enter a player's name, and you'll find a player's games played by position (without needing to know a player's team, as with several other sources out there. Note however that games played in the outfield are not differentiated by left, center and right field.
Another way to do this would be to have the commish of your league assign positions based on a player's most likely position in the majors. This involves some guesswork however, so I don't really recommend this.
Hope this helps. And whatever you do, make sure that everyone is informed of these positions well before your draft.