I agree with what you say concerning the kunai argument on one thing. The kunai can't extend chakra, so the chakra won't be connected if Minato were to throw it just like that, but Minato probably can infuse his chakra within his kunai and thus creating the area where his chakra would touch Sasuke within his Susanoo without going into it directly.
Also, he can do it by himself or the help of a clone. All he needs is to extend his chakra over a certain area while closing the range and it will warp Sasuke or/and his Susanoo depending on his intentions(like he teleported Kyubi and his TBB without contact and without teleporting Gamabunta who was in contact with him)
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When they reappeared, notice that Sasuke was even surprised and Naruto questioning himself about what happened
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Later when Naruto asked why he didn't teleport Hiruzen as well, he said it only works when he touches the target directly OR
when target(s) is(are) related to his chakra somehow
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So basically if you are in the area of his infused/extended chakra, he can teleport you without making contact with you
PS: Notice that this feat was made by Minato's clone, something that Minato can use. He even stated in this chapter that it had been a while since he used his new technique(that we will see in upcoming chapter), technique that requires the use of clone, which means it was part of his fighting style while alive