The consensus of the chachamim seems to be that one can (and should) be mekayaim the mitzva of tzitzis withOUT the techailes.
The correct source of techailes, is, as I’m sure you know, in doubt. There are those who feel they DO know the correct source, but there is machlokes even among those people as to what that correct source is.
Undoubtedly, the ideal way for tzitzis to be made IS with techailes, but rather than risk using the wrong dye, most poskim hold to do without the techailes altogether.
To answer YOUR question, by not wearing an arba kanfos AT ALL,in view of the above, we would STILL be mevatel the issue of techailes, AND we would be mevatel the entire mitzva of tzitzis.