Answer

You can search online. The later halakhic authorities have discussed this.
In my opinion, no. First, there are views that saying during the weekday to do something on Sabbath is not prohibited at all (if the prohibition is because of “speaking of such matters” and not because of agency to a non-Jew, as a stringency. There is a contradiction in Rashi on this). Second, logically, when for you it is a weekday and the non-Jew is in another country where it is Sabbath, this is less severe than telling a non-Jew on Friday eve to desecrate the Sabbath. Logic suggests that the determining day is your day, not his (since you are the one obligated to observe the Sabbath). One should remember that this is a rabbinic prohibition (apparently even lighter than an ordinary rabbinic prohibition), and therefore in a case of doubt one may be lenient.
If you benefit from the results, this could be considered an act done on Sabbath, and that is already a somewhat different issue (though here too, in my opinion, there is room to be lenient).