Hi Karin,
I think you can only clean slightly your blade without damage the crossgrain.
I leave out off US too and I use a very different product to clean my blades,the automotive paint polishing paste. It is a very slight abrasive product and I think it made the same Simichrome's results.
But be careful, like the Simichrome when used in excess it can damage the crossgrain and it's not recomendable to use it in etched areas.
I usualy find this product here in Brazil at car paint stores and I think there are similars in Europe too.
