First, not all job applications are created equal. While a section for disability is present on some, or even most job applications, particulary in the US, there have been several occasions where this section is not present, in which case the whole thing becomes quite a bit less cut and dry.

Second, by stating that just showing up with a cane would put them "in a weird spot" as you put it, you are in my opinion perpetuating the very thing the ADA is trying to prevent. Showing up to work with a cane shouldn't be "weird". it should be the most normal thing in the world, and if an employer gives a prospective employee trouble about same, that would be discrimination which you might as well unearth before you start there to begin with.

You say there might be "hurdles", and I absolutely agree that those should be mentioned. But everything has its place.

If there is no specific question in a job application that asks about disability, OP is under no obligation, legal or otherwise, to disclose that information at that point in time, and there are very legitimate reasons not to disclose this information quite yet. If anyone at the place of employ makes a thing of that, then this is not the place for OP to work, because if that wouldn't have happened initially it certainly would've happened later regardless of when this information was disclosed.. Christ, this is a visual disability, not a contagious disease. Do we have to indicate marital status and sexual orientation as well just to make sure we don't offend a manager's delicate sensibilities?

I don't believe in the "visually impaired people should bend over backwards to make sure they don't make the poor normies feel at home" rhetoric, I think it's an old-fashioned way of ablism that has no place in 2021.

Having said that though, I'm not saying one should outright lie about one's disability. If you think your disability will not hinder you in the job you are trying to perform, absolutely apply without disclosing. While it is true that the ADA prevents people from being denied due to disability, it does jack shit about employers lying about the reason for a rejected application, or about an HR rep quietly binning your application if they feel they can get away with it without causing a fuss. This happens here in Europe, and it happens just as much in the US, ADA or not.

If you do think your job will require some kind of accomodation, wait until you get invited for an interview, then either bring it up when you get the phone call to schedule, or when you are there in the interview room.

Why? Because at that point, you have far more control over the subsequent reaction. Stick a big fat blind sticker on your resume and people will have days, even weeks to decide you're not worth the fuss and figure out a creative loophole to get rid of you, or come up with a bunch of questions that will make them feel incredibly awkward because they won't have the means to answer them, which means their preconceived notions will answer them for you. You don't want that, believe me.

Have them find out when you're on the phone or in the room with them, and any questions or concerns they have can immediately be aired and dealt with. And I mean on the phone or in the room with an actual rep from the company, not some recruitor or intermediary. Disclosing it there will just cause an elaborate game of Telephone to happen which in the end benefits nobody.

I've been doing this job thing for the last 6 years, having worked for various companies in and out of the US both as a wage slave and a freelancer. This is the approach I've used for all of it, and purely as a social experiment I tried the much dandied about method of being good and letting people know at the earliest opportunity. I'll just let you guess at what method was more successful.