You could change your picture and change your character model with EE-keeper or the console... I don't THINK that would cause any issues. Adding abilities could sub for eyerays, but be careful which ones you add. Play around with it, just don't be too upset if it causes crashes or doesn't work.
Another aspect to consider is the circle size of the creature. The selection circle of a beholder or dragon won't let you pass any door or narrow passage. Then again, if you change yourself into a bat, squirrel or other creature with a miniature selection circle you may reach places that you aren't supposed to.
That's a great point. You could use the Gauth model and just call yourself a beholder to avoid sizing issues. This is definitely do-able though. I've seen Quasit and Mephit PCs on boards... just can't guarantee eye rays working as desired and at speed. Pictures and shapes are the easy parts, it's abilities and whatnot that'll cause you issues.
I've done that just as Jester said - changed my portrait and my appearance to a Mind Flayer, inspired by my forum avatar. And made him a Swashbuckler. It played a bit like this
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Then again, if you change yourself into a bat, squirrel or other creature with a miniature selection circle you may reach places that you aren't supposed to.
It played a bit like this