I’m not getting involved in the particulars of the shailah – my research on “Techeiles” consists of listening to one or two shiurim a year ago, and some minimal browsing online. I don’t profess to know anything about the Murex, or about Techeiles.
For years, I had shver why we don’t wear techeiles at least מספק. Surely the dictum of ספק דאורייתא לחומרא obligates us to wear something which MAY be the techeiles, even if we are not convinced that it is! I find it a chiddush to say that the fact we have no Mesorah stops any לידת הספק.
I think the answer to this is R’ Chaim’s vort. R’ Chaim explained that ספק דאורייתא לחומרא only obligates an action that will remove you from the ספק. For example – nobody who davens Nusach Ashkenaz will say Krias Shema in Sefardi or Temani pronunciation, although it is a חיוב דאורייתא and there is certainly a chance that the Temani mesorah is correct. So why doesn’t ספק דאורייתא לחומרא obligate you to say Shema in as many pronunciations as you can? The answer is – since even after you say Shema a second time, you still will not have ודאי been yotze the chiyuv, you are not obligated.
Once we establish that you are not mechuyav מדין ספק, you are only obligated if you really are convinced that you are wearing Techieles. And even if you are 100% without a shadow of doubt sure that the Murex is Techeiles, you still have no idea whether to wear them like Tosfos, like the Ra’avad, or any of the other shittas.