I clean horse saddles probably about 50-60 times a year and they are often worth between $2,000 - $8,000.... depending on the saddle.
The only problem about using dish detergent is that it's designed to cut through and remove grease and oil. You want to maintain the natural oil of the leather.
A more safe household product would be Murphy's Oil Soap (used for cleaning woodwork).
A tin of saddle soap is something like $2.00...most hardware stores and some grocery stores have it.
You could even grab a tin of neutral shoe polish for maybe around $3.50, also at many grocery stores.
I've never seen Dubbins sold anywhere in the USA.....not even in my horse tack mailers that I get spammed with constantly.