Japanese silk tie can be dry cleaned with "petroleum solvent" ("Sekiyu process"). How do I make sure it gets treated right?

The tie in question (dark green): https://ajitowaza.raku-uru.jp/item-detail/454458

I am guessing that this translates to a hydrocarbon solvent, but I'm not entirely certain. I live in California so perc is out of the question (unless I drop it off somewhere before flying home from NY state).

Background information: i was careful during the wedding but the cake box had icing on the outside