I am Japanese and would like to know the subtle difference in English between the next two .?

I am an English speaking American, and the two examples have the same meaning when writing a message . But when speaking the word "wouldn't" isn't strong as the word "No"

 # 1. "I would have no interest in it."  Is a clearer, because it has the words, "NO interest"

#2 uses the CONTRACTION "wouldn't", which means "would not" and might be a little less direct or a little casual compared to  using "NO"

I have no interest in it.

The second is not quite natural: we would say, "I wouldn't have any interest in it".

A is a little more formal, therefore a little more emphatic. But the meaning is the same.

The first form is reasonable English. The second form is unlikely to be heard from a native speaker of British English.

For me, the use of the second form would say 'Non-native user of English'.  But if it was "I wouldn't have any interest in it", that form is native, and possibly more often used than 1. 

For me in southern Britain there would be no difference in intention between 1. , and 2 with my addition of 'any'.

Await answers from Americans etc.

1.  I would have no interest in it. [Means the talker is uninterested in the subject.]

2. I wouldn't have interest in it. [Means the talker would never become interested.]

No difference, just a choice of wording.