1. Can you ride your bike the way that it is now? If your answer is "no" you have nothing to lose by trying to straighten your derailleur hanger. FWIW, I've bent back some pretty seriously bent aluminum hangers and have never had one break on me - yet.
2. How many rear cogs do you have? Up to 8, I can eyeball the alignment adequately. Don't try to bend the hanger without having a bolt in the derailleur mounting hole because you might ovalize the hole. I leave the derailleur in place and bend it with my hands if I can. Otherwise I clamp a big Crescent wrench over the derailleur. I don't even try that with more than 8 cogs because the cogs are so closely spaced that you have to be pretty accurate. I have the Park Tool alignment tool which works well.
3. If you don't have an alignment gauge, you are still in luck. The work around is to use your front wheel. Remove the quick release and screw your front wheel axle into the derailleur hanging hole. Make your front wheel totally parallel to your back wheel and you're good-t0-g0.
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My greatest fear is all of my kids standing around my coffin and talking about "how sensible" dad was.