To quote what has been already explained in the comments:
'I wouldn't know' here may be paraphrased I'm not in the situation where I'm familiar with what usually happens at Oscar ceremonies, as I'm not usually invited. – Edwin Ashworth
It means "Since I have not come here every year and it is the first time that I received the award, I am not sure whether you did it last year or the year before." – Rathony
The comment is meant to be a joke. "I wouldn't know" is a playful innuendo that hints at the fact he resents he had never won an oscar before despite his many nominations, so he doesn't know what the ceremony is concerning such an event.
Some equivalent expressions in Spanish would be:
- Y yo qué sé.
- ¿Cómo quieres que lo sepa?
You're right that would be too rude a comment to fit this case. Considering that and the fact DiCaprio isn't answering any question, a more appropriate translation would be:
- ¿Hacen/hacéis esto todos los años? Yo no tengo forma de saberlo.
The playful part of it is lost in translation, I'm afraid.
To explain this a little further, The Free Dictionary defines I wouldn't know thusly:
(I) wouldn't know: There is no way that I would know the answer to that question.
De ninguna manera podría yo saber la respuesta a semejante pregunta.
The conditional ("wouldn't know") is being used to express that if there's a cirumstance under which the speaker would actually know the answer to what they are being asked, such circumstance doesn't exist or it just isn't true. Let's take a look at an example from the same page:
- Bob: Are there many fish in the Amazon River?
- Mary: Gee, I wouldn't know.
Mary would arguably know the answer if she, say, had a passion for Amazon's fauna to the extent that she actually knew how many fish there are in the Amazon River. However, such condition is so infeasible that it's legit to say there's no way she would know the answer. In other words, if the most far-fetched condition one can think of were true, she still wouldn't know the answer. This is obviously a hyperbole, since there are some conditions that would allow Mary to know the answer, but saying there's none is a way to make her sound more contundent.
In Spanish, you wouldn't say "(yo) no lo sabría" in this case, but you can indeed say "(yo) no podría saberlo" or even "(yo) no sabría decirte". Even though it doesn't make much sense to translate it literally, the meaning is pretty much there if one does just a little mental acrobatics:
Under no condition would I know the answer, or I wouldn't know the answer under any condition = Bajo ninguna circunstancia podría (yo) saber la respuesta // Bajo ninguna circunstancia sabría (yo) decirte la respuesta.