"I'll tell them when I know more"
Here's a belief that sounds responsible. You'll tell them once you know. Once the result's in, once you've worked out the numbers, once you've decided what to do about the marriage. Telling now would be telling them a question. Better to tell them an answer.
Look at what the waiting consists of. The fortnight before the scan result is, for most people, the worst part of the whole thing. The result, whichever way it goes, is a fact to be dealt with, and people deal with facts. The fortnight is the private version at full size, every outcome at once, with no edges, at three in the morning. That's the stretch you've decided to do alone, and it's the stretch where a second person would have helped most.
There's a version of this that never ends, and it's worth naming. The scan result comes back needing another scan. The numbers get worked out and there's a new letter. The decision about the marriage turns out to be several decisions. "When I know more" is a horizon, and horizons move, and a person who's waiting for enough certainty to tell can wait for years, because there's always more to know. The mistake in the spreadsheet is the clearest case. You'll know more when it's found, and when it's found the telling will be an explanation to a manager rather than a confidence to a friend, and it'll be a worse conversation for having waited.
There's also what the waiting does to the eventual telling. A worry disclosed on the day it arrives is a worry shared. A worry disclosed after a month, with a result in hand, comes with a second thing attached, which is that you carried it for a month without saying. The listener hears the result and hears the month, and the month is the part that hurts them. "Why didn't you tell me?" is the question you're setting up by waiting for the answer.
Tell them the question. "I've got a scan result on Thursday and I'm frightened." "There's a letter from the bank I can't make work." "Something's wrong at home and I don't know what yet." Those are complete sentences, and they're the ones that get you company for the fortnight, which is when you needed it.