A Sword Has the Same Status as a Corpse

If one of the relatives of the deceased touched the corpse with his watch on, can he now enter a synagogue with the watch if there are Cohanim, given that the watch is made of metal, and ‘a sword has the same status as a corpse’, hence the watch is impure with the highest level of impurity (‘avi avot tumah’), and when he enters the room, all the priests become impure?

Priests have a custom to be lenient with the impurity of 'a sword has the same status as a a corpse'.

In Numbers 19:16 it is written, 'And whoever in the open field touches one who has been slain with a sword or who has died naturally, or a human bone or a grave, shall be unclean seven days.'
And it is said in the Talmud in Shabbat 101a, and in many places in the Talmud, 'a sword is considered as a corpse', meaning that the sword that touched a corpse itself is impure with the highest level of impurity. Halachic authorities disagreed on the law of 'a sword is considered as a corpse'. The Rambam's opinion is that it applies to all clothes and vessels that touched a corpse except for earthenware vessels, but the Raavad's opinion is that it applies specifically to metal implements.
And indeed, halachic authorities quoted Tractate Semahot [Chapter 4] 'Any impurity that the Nazirite does not shave for, the priest is not warned about it (that is, there is no prohibition to become impure).' (Even though the version that we have is 'For any impurity from the dead that a Nazirite has to shave for, a Cohen is punished with forty lashes, and for impurity that a Nazirite does not shave for, a Cohen is not punished with forty lashes.')
And the Remo wrote in chapter 369, paragraph 1, and I quote: 'Some say that priests are forbidden to become impure with a sword that became impure with a corpse (Kol Bo in the name of Sefer Yereim and Responsa Rashba in the name of the French Rabbis), and some are lenient (Responsa Rashba there in the name of the Raavad and see Tosafot Nazir at length), and so they have a custom to be lenient and they are not cautious about this. And halachic authorities explained that those who forbid and those who permit disagreed whether a Nazirite who became impure with 'a sword is considered as a corpse' interrupts his count or not, for those who forbid hold that the Nazirite shaves for this and therefore a Cohen is forbidden to acquire this impurity and such an item imparts impurity even in through a tent. And those who permit, permit it because in the Tosefta Chapter 1 of Ohalot it is explained that the Nazirite does not shave for this, and consequently a Cohen is not prohibited from acquiring this level of impurity.'