The SE's will have bleeder resistors, and the flyback is likely one of the 'newer' ones that bleed off. Honestly, it's not a big deal, no need to be daunted - we just wouldn't want someone launching in there and taking things apart while still plugged in or when things haven't sufficiently discharged. If you wait a bit (a couple hours, even less) after unplugging it, it's totally fine to handle. It sounds like you're the cautious type, so I think you'll be totally fine to open things up and take a look around. You can find out a lot with just your eyes and a multimeter. So go ahead and do it - it's totally worth it.
I'm not familiar personally with the 'slow die'... but based on what you're saying it sounds to me like your logic board is fine, and probably the power supply is fine as well. The 'poof' sound is, I expect, just the sound of the system switching to desktop in the absence of a working tube.
To be sure about the power supply, you can verify the voltages via the floppy port... simply sticking a paper clip or stiff wire into a hole along the top row of the floppy port at the back and measuring the voltage with a multimeter each time (red to the pin, black in one of the port screw holes - any one will do, they're all ground) while the machine is on... I can't remember the order, but you should see around 12V, -12V, and 5V on some of them. Just be careful not to accidentally cause a short, it can do damage to the logic board. Just be deliberate with your actions and take your time... as with most things.
This book isn't perfect, but it's a good place to start, and has a lot of good info in it about safety, what values to measure for, and how to and diagnose issues - which pins on the floppy port to test and how to do it - as well as some specific info about the SE:
http://www.maccaps.com/MacCaps/Repair_books_files/Macintosh Repair and Upgrade Secrets.pdf
The nice thing about analog board issues is that they're usually pretty easy to fix, and the parts are mostly cheap and easy to find. The big exception is the flyback, which have become nearly impossible to find new, and they're crazy expensive ($150USD+) when they do show up. But you can usually find a donor board here in the trading post or on ebay for a decent price.