At an uncontrolled airport, where you take off is up to you, the airport owner and your insurance company. There's nothing stopping you from taking off from any surface, as long as you respect government regulations against causing a danger to others (say your taxiway departure scares somebody and they complain), the wishes or policies of the airport manager or owner who implicitly grants you permission to use the facility, or your insurance company's policies on use of unlicensed surfaces.
As far as the regs go, generally the pilot's decision to use a particular surface is deemed to designate that surface an "aerodrome". But use of taxiways is rarely done because it's simply bad etiquette and there's a better surface nearby, so it would be pretty rare outside special circumstances.
On the other hand, in winter in North America, you will have ski planes using areas off the runway, usually parallel to it, to operate from, maybe on the opposite side to a taxiway.
Your actions were perfectly reasonable, but myself as an ex bush pilot used to operating off-airport (lakes mostly) I'd have used the taxiway if there was nobody else around.