You could do an Ansari-Bradley test or a Seigel-Tukey test ... or indeed almost any suitable scale test.

To estimate the scale, you can scale one sample until the test statistic reaches its expected value under the null hypothesis, and you can get an interval for the scale by the same method as generating an interval for the shift parameter in the Mann-Whitney.

You could do an Ansari-Bradley test or a Siegel-Tukey test ... or indeed almost any suitable scale test.

To estimate the scale, you can scale one sample until the test statistic reaches its expected value under the null hypothesis, and you can get an interval for the scale by the same method as generating an interval for the shift parameter in the Mann-Whitney.