Reish Lakish says that a Mitzvas Aseh does not supersede a Mitzvas Lo Sa'aseh if it is possible to fulfill both the Aseh and the Lo Sa'aseh. (1)
A Metzora must shave his head with a razor even if he is a Nazir. (2)
A Metzora must shave his entire head including his Payos because the Aseh supersedes the Lo Sa'aseh of cutting of the Payos. (3)
A Metzora must even shave his beard because the Aseh supersedes the Lo Sa'aseh of cutting of the Payos.
The Mitzvas Aseh of Tzitzis supersedes the Mitzvas Lo Sa'aseh of Sha'atnez. (4)
A BIT MORE
1. Therefore if it was permitted for a Metzora to shave his hair without a razor it would be forbidden for him to shave his beard with a razor.
2. Even though it is forbidden for a Nazir to shave his hair with a razor the Mitzvas Aseh of a Metzora shaving his hair supersedes the Mitzvas Lo Sa'aseh and Mitzvas Aseh of a Nazir shaving his hair.
3. Shaving off the entire head including the Payos is included on the prohibition of cutting off the Payos.
4. Therefore one may place Tzitzis of Techeles (blue dyed wool) on a Talis of linen.
THE SHAVING OF A METZORA
A Metzora must shave his entire head including his Payos and his beard because an Aseh supersedes a Lo Sa'aseh. Tosfos asks how we know that a Metzora who is a Nazir must shave off his hair. In this case there are two Mitzvos Lo Sa'aseh (shaving the Payos and cutting the hair of a Nazir), and one Mitzvas Aseh (Gidul Pera of a Nazir) and maybe a Lo Sa'aseh does not supersede two Mitzvos Lo Sa'aseh and an Aseh! Tosfos answers that the Chachamim learn out from the Pasuk that a Metzora who is a Kohen may shave his beard even though there is a Mitzvas Lo Sa'aseh and an Aseh. Once we know that an Aseh supersedes a Lo Sa'aseh and an Aseh it will also supersede two Mitzvos Lo Sa'aseh and an Aseh.
SHA'ATNEZ WITH TZITZIS
It is forbidden to place Tzitzis of Techeles (blue dyed wool) on a linen Talis. Instead only white linen strings shall be placed on the line Talis. This is not because the prohibition of Sha'atnez is paramount over the Mitzvah of Tzitzis, but rather because the Rabanan decreed that it shall be forbidden because of the possibility that one may wear the Talis at night, which is a time that the Mitzvah of Tzitzis does not apply, and he will consequently transgress the Mitzvas Lo Sa'aseh of Sha'atnez. (Rambam Hilchos Tzitzis 3:7)