First, it is worth noting that the appearance of it being a "near miss" is misleading. The USS Indianapolis was sunk going west of Tinian, an area that was much more dangerous that sailing east of Tinian from the perspective of submarine threats. Which is to say, the fact that it was sunk a few days after dropping off its cargo does not imply it had an equally high chance of getting sunk before it did so. It did not.

As for the contingency plans: the Indianapolis only carried the components of the uranium bomb (including 60% of the high enriched uranium core). The US had a separate supply line for the plutonium bomb (whose parts were sent by cargo planes from Albuquerque). It would have delayed the use of the first atomic bomb by several days at most (e.g., August 9th rather than August 6th, assuming it was the same schedule as with it); it would have delayed the use of a second atomic bomb by about 10 days (e.g. August 17-18th). Which is to say: not a huge distinction in respect to the Allied plan, esp. since most historians don't think the second atomic bomb use had much impact on the Japanese surrender decision. It strikes me as quite likely that the only "major" result would be that the war would have ended with only one atomic bomb being dropped on a city, instead of two. I suppose that's a positive result (ironically?).

From the perspective of the Manhattan Project planners, the boat method was much safer and less chancy than the long-distance planes — they actually broke the remaining 40% of the Little Boy core into 3 separate pieces when it sent them by plane, to spread the risk around (losing any one of them would be much less disastrous than losing them all).