You can only get a rough comparison without a spectrometer, but a controlled photo test can help.

Use a known neutral target first: a grayscale/neutral patch is useful for checking whether the light stays neutral from shadows to highlights. A ColorChecker already includes such patches. Carefully block ambient light and keep geometry consistent, since angle, reflections, and mixed light can hide real differences.

A ColorChecker is more useful for building a custom camera/light profile than for judging by white balance alone. Correcting WB from one white patch does not fix all color errors, because poor-spectrum lights can shift different colors in different ways. That’s why two lights can look similar after WB but still render reds/cyans differently in practice.

For a better comparison:

• light the target evenly with one light at a time
• keep exposure and framing consistent
• include neutral patches and a range of colors
• avoid wall reflections and other spill
• if possible, use software that recognizes the ColorChecker and creates a custom profile

Then compare how much correction is needed and whether colors remain consistent after profiling. In short: your idea is valid, but white-balance-only testing is too limited; a ColorChecker plus proper profiling and a controlled setup is the best DIY approach from the options discussed.