I have no idea which widgets have a getDC() method

Afaik, none of them do. A quick grep of the docs suggest that the following have a GetDC(): Wx::EraseEvent, Wx::HtmlWinParser, Wx::Printout. I think there are two ways of achieving what your're after (maybe more) - either use a Wx::ClientDC:

    my $dc = new Wx::ClientDC($frame);
    $dc->DrawLine(...);
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or set up a Wx::PaintEvent for your frame:

    use Wx::Event 'EVT_PAINT';
    EVT_PAINT($frame, \&OnPaint);

    sub OnPaint {
        my ($frame, $event) = @_;
        my $dc = new Wx::PaintDC($frame);
        $dc->DrawLine(...);
    }
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See Wx::Perl::Throbber for an example of the latter.

The wxPython wiki has lots of useful examples. They're in Python obviously, but it's trivial to do the translation in your head.