The dialect is American English, but I'd be interested to know if this varies between dialects. Is it"togglable" or "toggleable"? Because neither dictionary.com, webster.com, nor Outlook's spelling suggestions/checker tend to have any record of this word. I have a hard time believing it's not a word in proper English though, and I would be tempted to think its spelling is "toggleable".
It's not a word, so it has no formal spelling as of now. The English language's main strength is its adaptability, so one day it will most likely be officially accepted as a word, but for now, it has no defined spelling.
I would personally keep the e, as there are 3 consonants before it, and that makes me want to balance the scales a bit, and that's how it works in some others with the same scenario, like settleable, whistleable, and handleable.