Rebbe,
We learned that if a person is modair hanaa (swears not to take hanaa from) a particular kohein then that kohein shouldn't bring his korban. Haven't we learned elsewhere that if a person swears not to take hanaa from a person he can still be yotze his davening as a sheliach tzibbur or his layning. The reason given is mitzvot lav l'hanot nitnu. Why would the case of the kohein be different?
B'kavod,
Sam Kosofsky
It seems that the difference is that when the Kohen offers the Korban the owners do in fact receive physical Hana'ah, not merely the performance of a Mitzvah, because the fact that the Kohen brings the Korban makes it possible for the owners to eat it. This seems to be the intention of TOSFOS 19b DH MI, who writes that there is no ramification for the question of whether the Kohanim are our agents or Hash-m's agents regarding whether the Kohen can offer it for a Mudar Hana'ah, because the Kohen always gives Hana'ah to the owners of the Korban. RAN NEDARIM 35b DH HA states this rather more explicitly that the Hana'ah being discussed is is that he thereby becomes permitted to eat the Korbanos, i.e. before he received his atonement he was forbidden to eat Kodshim but now he is permitted.
The above concept is similar to the Gemara in ROSH HASHANAH 28a that one may not do immersion for a Mitzvah in the summer in the water of someone one whom he is Mudar Hana'ah from. Even though this is a Mitzvah nevertheless, since the body enjoys cooling off, it is forbidden.
KOL TUV
D. Bloom
I have to correct what I wrote in answer to this question. The reason why in fact we do not say Mitzvos Lav Lehanos Nitnu when the Kohen offers the Korban of the Mudar Hana'ah is because since the Kohen is doing the Shelichus of the Mudar Hana'ah, this is considered that the latter derives benefit from the former. The source for this is NEDARIM 36b where the Gemara says that if the friend seperates Terumah from the fruit of the Mudar with the knowledge of the latter, this is forbidden because "ke'Mehanei Lei de'Avid Shelichusei" - he gives him Hana'ah by performing his mission. RAN DH ELLA writes that whenever he does someone else's Shelichus, this is considered that he is giving him Hana'ah.
Your question is in fact raised by TOSFOS NEDARIM 35b DH IBAYA who writes that certainly the actual Korban is a Mitzvah (and therefore one should have said Mitzvos Lav Lehanos Nitnu) but since the Kohen is his Shaliach for this, it is forbidden. Tosfos' intention is to the above stated Gemara 36b, that since the friend did what the Mudar asked him to do, this is considered Hana'ah and is therefore forbidden.
See RAN ROSH HASHANA 7b in RIF pages DH OMAR RAVA who writes that even though the Gemara there 28a states that it is permitted to blow the Shofar on Rosh Hashana for a Mudar Hana'ah, nevertheless this is only if he blew it without being asked, whilst if the Mudar asked his friend to blow for him, this is forbidden because he performs his Shelichus as stated above. SHULCHAN ARUCH OC 589:7 rules according to RAN.
Therefore, according to this, it shold follow that the Kohen is only forbidden to bring the Korban if he was asked to do so and that the Chazan may only be Motzi the Mudar Hana'ah with Davening, or the Baal Keriah with Krias ha'Torah if they were not specifically asked to do so.
(What I wrote last time that it is considered that the Yisroel receives Hana'ah from the Kohen because he enables him to eat the Korbonos, is not correct because RAN NEDARIM 35b DH HA in fact writes that this is only considered indirect benefit (because the Yisroel only acquires it after the Kohen brings the Korban) and therefore is permitted. See also RITVA YEVAMOS 103b DH VE'SANDAL and note 283 there)
KOL TUV
D. Bloom