Shotcut does not require all your source material to be the same frame rate. Shotcut will skip/duplicate frames in your source files to match the project frame rate.
The key is to set a Video Mode with the final frame rate that you want when you start your project.
For some frame rate conversions, the simple skip/repeat capabilities in Shotcut can result in jerky motion (for example, 25fps to 30fps). In that case, some people choose to use the Motion Compensation conversion in the Convert-to-edit-friendly tool.