I would use a buttercream that didnt have any butter, just all shortening. Shortening holds up alot better in hot conditions compared to butter-based buttercream.
But I think you should explain it to the customer and if they insist on buttercream, just go that route. Also, to reduce the amount of time the cake is sitting outside, you should probably time the dropping off of the cake close to the start of the reception. Even though the shortening-based buttercream holds up better you still wouldnt want the cake sitting outside for hours and hours.
Hope this helps