Instead of g sharps use a flats, it's much easier to read with no need for the natural sign either (a flat is harmonically correct too). Spelling is extremely important for players and also harmonically for the music, voice leading relies on it and the musicians sense of 'place' relies on it. It is especially important for strings where the difference between the same note spelt differently can have an effect on tuning because of finger placement.
A key change should be reflected on the stave with a new key signature and unless there is chromaticism outside of the new signature, accidentals will not be required. The same principles here apply to all music and instruments.
In general both is possible:change the keys as done in your first post, or using accidentals.
If using accidentals, use flats if the key you are in uses flats. Or use sharps when the key you are in uses sharps. So in your second example it would be better to use "a flat" instead of "g#".