On the one hand an oinen is exempt from all mitzvos, however, some say (Shemiras Shabbos, Perek 64, he’orah 75 in the name of the Kol-Bo, Hilchos Aveilus, 2:11, pg. 124) that perhaps it is kavod hames [honor for the dead body] to make sure nothing dangerous happens on the way. The Shu”t Afraksta D’Enya (Vol. 3, siman 218) also writes this logic.
R' Elyashiv said it’s very likely that when Chazal said an oinen is exempt from mitzvos, they meant that he is exempt from fulfilling mitzvos b’Toras mitzvah [mitzvos simply for the sake of the mitzvah], if, however, one feels a need to beseech and ask for mercy from the Ribbono Shel Olam for his journey then he may daven. Just like if an oinen has a headache, he may ask for mercy (daven), the same thing is with Tefillas HaDerech.
According to the Chavas Da’as (Yoreh De’ah 110, Beis HaSafek, s.k. 20) in such a case one may even finish with the berachah, בא"י שומע תפילה(cited in Kanfei Ruach, Perek 17, he’orah 3). R’ Zilberstein (Kanfei Ruach) adds: The Gemara says that Tefillas HaDerech has the status of המלך בקונך וצא – asking permission from the King before traveling. If we look at it as asking permission to travel, then just like an oinen may ask permission from a human being, similarly, he may ask permission from Hakadosh Boruch Hu.
However, some say an oinen is exempt from Tefillas HaDerech (R’ Sroya Davlitzky, Kuntros Tefillas HaDerech, siman 10), and some say, that even if he recites Tefillas HaDerech, he should only say the main berachah and not the pasukim that people normally add. (Ohalecha Be’amitecha 9:9)
