Yoma 33 Touching your Tefillin

The Gemora on 33a cites Rish Lakish that one is not permitted to pass over a mitzvah and that is why the kohen cleans the mizbeach before the preparation of the menorah for the mizbeach is closer to the entrance of the heichal. Rava (33b) states that we can learn from here regarding tefillin that the shel yad should be before the shel rosh. Rashi says that this is referring to the putting on of the tefillin for the arm comes before the head. Rabeinu Tam disagrees and says that it is referring to the removing and placing in the bag, that the shel rosh should be placed first in order that the next day, one should come into contact with the shel yad first. Rabeinu Eliyohu learns that it is referring to the touching of the tefillin during davening. The Shemuas Chaim learns from here that it is not sufficient to touch the straps of the shel rosh, rather one is obligated to touch the bayis itself, for otherwise - one could touch the straps first and then touch the shel yad, for he is not passing over any mitzva.

Is there an inyon perhaps to touch the bayis of the shel yad itself and not merely the sleeve which is covering the shel yad?