Skeeter did it
Many, many years ago, legendary gun writer Skeeter SKELTON did a project to convert the COLT 1903 .32ACP to .380ACP. The result worked, but if I remember write, it was not worth the effort. You could find a .380ACP 1908 model for less effort.
I see .380ACP models around on a regular basis, so I would just look into trading a 1903 for it.
If you just want a shooter, the .32ACP really shoots well in the 1903. The only real drawback are the sights (too small) and the safety is too small.
Jim