If you want the change from one file to the other to be seemless, you could do

use File::Copy qw( copy );

copy($old, "$old.bak")
   or die("Unable to backup \"$old\" to \"$old.bak\": $!\n");
rename($new, $old)
   or die("Unable to replace \"$old\" with \"$new\": $!\n");
[download]

If the new and the old (original) file are on the same volume, there will never be a time where the file is missing or incomplete.

Update: I think I misunderstood "B*" and that this doesn't answer the question.