First, why do you say your research suggests you "need" a survey? Is that some regulatory or HOA approval that is required? If so, you may not have a choice.
Second, I agree with others that the survey is cheap insurance. If you put the fence on your neighbor's property, they can force you to remove it; if you put it too far on your own, the neighbor may ultimately be able to claim title to that strip (or, at a minimum wrap you up in litigation over it). In all likelihood, none of this will ever happen. But fences tend to last for a lot longer than individual neighbors, so keep future-you-with-new-asshole-neighbor in mind as you make that decision.
I'd suggest talking to your neighbors -- who knows, they might even be willing to split the cost of the fence and/or survey if they have been thinking of doing the same thing.