I will throw in a different perspective - if you school does not offer AP courses (many strong independent schools do not) - then self studying and taking the exam should be viewed in a positive light by many colleges.
To not give away my children’s school - but a competitive private school often brought up on CC due to college placement rates does not offer AP courses - yet 40% of the graduating class report at least 2 AP scores of 4 or 5. This is listed in the school profile with the majority for Calc A/C, B/C, Chem, Comp Science and US History. So, to be a more competitive applicant from this school - you need to self study and take AP tests.