Well considering the differences in the two universes, Tapion gave Trunks the sword in the 'Present' Timeline, he could have done it in a different way in the 'Future' Timeline, it is largely unknown what happened before the Androids in the 'Future' universe. Although it's easy to assume it was the same until the androids appeared, there are differences in them before then, this is one of them.
In the 'Present' timeline Tapion gave Trunks the sword after the whole Buu thing, between 273 and 274 (dubbed) and he uses it in GT.
[FICTIONAL EXAMPLE]: In the 'Future' timeline, Hoi appeared after the Garlic Junior Saga. Tapion is freed and so is Hildegarne, Goku isn't around but fortunatley the Hildegarne in this universe is much weaker. It is killed by little Trunks (no fusion) and Tapion gives him the sword as a token of appreciation. Then the androids appear, Trunks fights them as best as he can but loses, comes back home, goes to the Present Universe, and the Trunks Saga begins.
No doubt one of you will find a hole in there but it could've happened like that.