You might have an [XY-problem][1] in that what you perhaps want to achieve is feeling natural and at ease when talking to babies, not necessarily avoid using a high-pitched voice per se. But using a high-pitched voice, you feel a bit silly and self-conscious, as if putting on a show. 

Now if the advice is "just talk in a normal voice", that's valid to the extent that you are certainly *allowed* to act natural; but in a [strange paradoxical twist][2], you will become very aware of your behavior, probably start to **act** natural in the sense of play-acting, and feel self-conscious again. 

Whatever you do, it will feel unnatural. 

You mention you rarely talk to babies. I guess then your lack of experience is responsible for the awkwardness. I for sure felt awkward with babies before people started to have babies all around me.

My first advice is therefore to have more experience with babies. My second advice is to defuse the awkwardness with humour. Paradoxical situations can be coped with using paradoxical solutions: Either go overboard with baby talk (OK, don't overdo it to the extent that it may look sarcastic), or vice versa exaggerate the serious person talk ("Good afternoon sir, how do you do?"). 


  [1]: http://xyproblem.info/
  [2]: https://en.wikipedia.org/wiki/Double_bind