I would like to know if it is ok to tie chabad, but alternating between white and tekhelet. That is, start the first wrap with white and the second with tekhelet and the next with white and so on.
The various methods of tying tzitzit stem from the various interpretation that the poskim applied when trying to understand the Rabbinic directives given in the Talmud. All the methods fulfill the Torah obligation which requires only one “kesher elyon” (upper knot) and one chulya of three wraps. So on the one hand you will be applying an integration of two accepted poskim (the Radzyner/Chabad and the Raavad) which would seem to be safe to do; on the other hand each of those poskim had their reasons for their complete method and so we can’t necessarily mix and match without running the possibility of making internal contradictions.
Now, in the Radzyner method, he holds the chulyot to be wraps of 3 and thus demarcates them by looping the shamash around every triplet. This is in CONTRADISTINCTION to the Raavad who holds the chulya to be a minimum of 7 wraps (4 white and 3 blue). And so if you were to some how try to make triplets you would be creating an internal contradiction in your definition of what a chulya is!
Thus, I would recommend not combining these two methods.
– Mois Navon