I don't think it's a matter of grammatical rules as such, but personally I don't like the "double negation" involved in juxtaposing not show + otherwise. That aside, consider these simpler examples...
1) Don't move or I'll shoot (1530 written instances in Google Books)
2) Don't move otherwise I'll shoot. (one written instance)
3) Stop! Or I'll scream! (297 written instances)
4) Stop! Otherwise I'll scream! (no written instances)
...where obviously #2 and #4 are vanishingly uncommon compared to #1 and #3, regardless of whether the first "alternative" involves a negated verb form.
In OP's exact context, I also don't like the use of will for the hypothetical/counterfactual second alternative. Again, I'm not convinced it's actually "ungrammatical", but I think would is far more idiomatic when referring to a "theoretical possibility" that (in context) definitely won't happen. Taking those two points into account, the smallest change to make OP's example idiomatic for me is...
5) We don't show this in the report, or xyz would happen.
...but I think on purely semantic grounds I'd rather use a conjunction that more accurately expresses the relationship between the two alternatives...
6) We don't show this in the report, because xyz would happen [if we did].
Note that when the first alternative is expressed in the negative as above, it's completely optional whether to explicitly specify if we did [include it in the report] because it's contextually obvious (if the first alternative is NOT X, the second one is usually just the non-negated X). But if the first alternative isn't negated, you'd normally need to be more explicit for clarity...
7) ?We put that in the report or the auditors would complain. (to me, "less-than-ideal")
8) We put that in the report because otherwise the auditors would complain. (better)
9) We put that in the report because the auditors would complain if we didn't. (best)