#Pyth, <s>64</s> 49 bytes

    jdhfqzsTsm^+msXtjCk2U2"<>""
    \r.1"",<..>,"dlz

This is the brute force approach, generate all sequences and check whether any sum to the input. Fish diagrams compressed as characters, whose binary representations are the `>` and `<`.

Some characters are stripped above, because control characters are used. They are reproduced faithfully here:

[Test case.][1]

xxd output:

    0000000: 6a64 6866 717a 7354 736d 5e2b 6d73 5874  jdhfqzsTsm^+msXt
    0000010: 6a43 6b32 5532 223c 3e22 220a 5c72 1214  jCk2U2"<>"".\r..
    0000020: 161d 2e31 2222 2c3c 2e2e 3e2c 2264 6c7a  ...1"",<..>,"dlz

  [1]: https://pyth.herokuapp.com/?code=jdhfqzsTsm%5E%2BmsXtjCk2U2%22%3C%3E%22%22%0A%5Cr%12%14%16%1D.1%22%22%2C%3C..%3E%2C%22dlz&input=%3C%3E%3C%3E%3C%3E