There is no difference between you saying “In sha Allah” or “Bi idhnillah.” That is for several reasons which are detailed below.

Uncertainty as to whether an oath was sworn in the first place – such as being uncertain as to whether the oath was sworn, or whether it was sworn and broken – in this case, nothing is required of the one who is uncertain, because the basic principle [and what is certain] is that one is under no obligation, and certainty cannot be dispelled by uncertainty. An oath does not become binding merely by thinking about it; rather it is essential that it be spoken out loud.