Changing Keys Without Changing Already Written Notes

Hello,
In the jazz band that I am in, one of the songs that we are playing is missing a piano part that was lost. The piano part is still in the score so I went and took photos of the piano part in the score so I could copy it over to Musescore 3 manually. All that I am doing is copying. The piece is in C major but it switches into Bb major at the solo section and then switches back to C major. I forgot about the key change and wrote the whole piece without ever changing the key. I noticed this when I saw that one of the whole measure chords had a natural sign next to an E even though it is in C major. If I had switched it to Bb major, that note would normally be a Eb and the accidental would change it to an E. Now here is the problem, I went and added the key change to Bb major and it added or subtracted accidentals to all of the following chords to make them in the original key of C major, even though I changed the key to Bb major. I was wondering if their was a way to change the key without changing the notes. I could just delete it all, change the key, and wright it again, but I was wondering if their was a better way to do this.

Thanks,
Noah