Firstly, I need to run 2 subroutines if my open fails, the code I have come up with works but seems clumsy.

This looks like an appropriate spot to use $SIG{__DIE__}.

{
    local $SIG{__DIE__} = sub { One(); Two(); die shift; };
    open TST, ">>$var1" or die "Can't open file: $!";
}
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The code would also run if your script dies in the block for an unforeseen reason. Well, I can't imagine anything that could cause it in this simple example :-) but it's a useful technique for the toolbox.