The language supports exceptions (panics). You could do something like (this is untested code):

  func panicBinaryWrite(w io.Writer, b binary.ByteOrder, data interface{}) {
    if err := binary.Write(w, b, data); err != nil {
      panic("Error in binary.Write")
    }
    return
  }

  func panicWrite(w io.Writer, data interface{}) {
    if _,err := w.Write(binary.LittleEndian,data); err != nil {
      panic("Error in io.Writer#Write")
    }
    return 
  }

  func ignoreErrors(f func()) {
    defer func() { 
      _ = recover()
    }()
    f()
    return
  }

  func (g *Gopher) DumpBinary(w io.Writer) {
    // Ignore all errors
    ignoreErrors(panicBinaryWrite(w, binary.LittleEndian, int32(len(g.Name))))
    ignoreErrors(panicWrite([]byte(g.Name)))
    ignoreErrors(panicBinaryWrite(w, binary.LittleEndian, g.Age))
    ignoreErrors(binary.Write(w, binary.LittleEndian, g.FurColor))
  }