Setting locale into application scope

I want my default date format to be iso8601 but I want my desktop panel clock to use a 12-hour display. For this preference, the MATE panel clock applet wants a session language that includes a 12-hour clock. To get the iso format, the recommendation is for en_DK and this, apparently, does not offer a 12-hour clock. How can I give the clock applet a locale with a 12-hour clock and keep the iso format everywhere else? I suppose I could set the bash session to en_DK and then applications run in that session will inherit that locale? But I prefer to make it a panel-specific locale.