This is a question with a number of layers, and ultimately there is no 'right answer'.
First, there are the legal provisions. Details will probably vary between countries and between institutions, but in general the law will stipulate that an individual with a declared disability has priority where two (or more) candidates are equally well-qualified. Unfortunately, in academic contexts this is somewhat meaningless: ranking candidates is inherently subjective, and it is always possible to find reasons why Candidate A is "better" than Candidate B. It would be unusual for a well-briefed committee to end up in a position where the disability laws determine the result.1
Second, there may be various other policies that come into play. For example, in the UK it is common for employers to guarantee an interview to any candidate who declares a disability and meets the basic requirements of the role. This may improve your chances, especially if you think you come across better in interview than you do on paper. On the other hand, you may waste time and energy if you are called for interview in circumstances where you're clearly uncompetitive.
Third, many institutions and individuals are increasingly focussed on EDI and access issues, and contextual information may be considered (formally or informally) during hiring/admissions decisions. Disclosing a disability may sway the committee in your favour, especially if you end up neck-and-neck with some other, non-disabled, candidate.2 On the other hand, you open yourself up to the possibility of negative discrimination: given the subjectivity of the process, a (consciously or unconsciously) biased committee member will be able to find a defensible reason to argue against offering you the position.
Fourthly, there are human factors. In your question, you write "I would not want to get... accepted merely due to my disability". Is this something that is going to prey on your mind every time your hit a rough patch in your research? Will you worry that your supervisor never really wanted to take you on? Only you know the answer to those kinds of questions.
Ultimately, there isn't a clear answer to your question: there are arguments both for and against disclosure at the application stage,3 especially if your disability does not directly impact the things that the committee will be assessing you on. Note that you can make different choices in different applications: for example, you might decide to take one approach when applying for a programme that recruits 10 people from 200 applicants, and another when applying for a position that will recruit one person from 20 applicants.
1 An exception might be some very large schemes, such national PhD funding competitions covering a wide range of subjects, where there may be more reliance on ranking candidates according to some numerical score (e.g. GPA).
2 This is not quite the same as the first case: you would not be chosen because the law says so, but rather because the committee felt your achievements deserved to be given a higher weight by virtue of the additional challenges you have faced.
3 You can always disclose your disability later in the process, e.g. upon being called to interview or after appointment.