I have used StarA's RTW tickets extensively in the past few years. I have never bothered to reissue if it's only schedule changes or simple routing changes without stop-overs. And UA is particularly accommodating domestically in this regard. However, I'm far more careful when it comes to international routing, especially on another airline.

I'd suggest that you call SQ to confirm the changes and see if they are happy to accept the changes you've made.