For the cut, tinsnips (e.g. "aviation snips") of course. These are churned out by Chinese factories and sell cheap anyplace on Earth. If the material isn't very heavy ordinary scissors work fine too, go figure.
This tool, guided by a straightedge, will make very accurate cuts and doesn't warp material or leave burred and serrated edges like snips do. It's mainly for scoring brittle plastics for snapping, but can also be used to scratch through soft metals in several passes.
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A pipe-to-plate butt joint will be crazy fragile. Is it possible to punch an undersized hole out so it looks like a crater? Then you can jam the pipe through (tight), solder to fill, and cut off the excess. I know you said it can't be done on account of the angle, but why not just bend the copper pipe, or even bend both pipe and plate (locally) after the joint's made?