R’ Hershel Schachter shlita holds that since there’s nothing to lose by wearing it, you should wear the techeiles nowadays.
R’ Elyashiv zt”l was against it, as he held we did not have a mesorah for it, and so shouldn’t do it.
R’ Chaim Kanievsky shlita holds that we won’t get techeiles until Mashiach comes, so the one we have is wrong. He also says, however, that he feels there is room to disagree with his view, and that if someone believes it is the correct techeiles, they have a chiyuv to wear it. (This differs from R’ Elyashiv, who said that even if we believed it was correct, we shouldn’t wear it due to a lack of mesorah for it.)
At the end of the day, as usual, one should ask their own Rav what to do, as there are gedolim on both sides of the issue on whom to rely.