However, some want to say as follows in the name of R' Chaim. We only say ספק דאורייתא לחומרא when by doing an action we can be מברר the ספק. Take the classic case of a person forgetting whether he benched, said shema, etc. or not. After doing the mitzva again he will be ודאי יוצא the mitzva and therefore he is חייב to do that. However, in the case of techeles, even if a person is machmir and puts on techeles he is not מברר the ספק. He still may not be יוצא the mitzva. The only time you say ספק דאורייתא לחומרא is when by doing something you can be מברר the ספק, however, if doing something leaves you in the same state as before, ספק, the principle of ספק דאורייתא לחומרא doesn't apply.
There are a number of problems with this analysis.
1. RHS and others claim that R' Chaim never said it, it is not printed anywhere.
2. Even if R' Chaim actually said it we don't pasken like this. The Rishonim have a machlokes whether the first 3 berachos of bentching are מעכב one another. What is the din if you only know 1 beracha, should you say it? The Rif says no because they are מעכב one another and the Ramban says yes that they are not מעכב one another. להלכה what should a person do in this situation? This is the same kind of situation as we described above with techeles. You have a ספק whether you need to say the beracha you know and even after you say it the ספק still stands, you still may have not been יוצא. The פמ"ג says that in this situation you don't say ספק דאורייתא לחומרא (like R' Chaim). However, there is one extra wrinkle here by bentching. By bentching if you are not חייב you are saying a ברכה לבטלה which is an איסור. In other words here the chumra is not risk free. Therefore the פמ"ג says that you should not say the 1 beracha. However, wearing techeles is risk free, therefore it would seem that even the פמ"ג would agree that you should be machmir.
In any case, both the Mishna Berura and the Aruch Hashulchan pasken against the