Oh, well in that case, not sure what to recommend as far as timing is concerned.
I have always, however, found it is much better for the surviving animals to actually see that their housemate is gone. Sounds macabre, but they seem to fret much less if they see the body... Seems that they understand better what is going on and that they will no longer see their friend around. Before I started doing this I have had animals go into extreme decline and/or go missing as they search for the departed one. Since I have done it, they have mourned a couple of days and then got on with life.