If you can find appropriate data, go for it. In general, the US data on swordfish and most HMS are extremely bad. WE have world record commercial catches of most HMS speices. Landings data are in numbers while weigh out are in pounds but do not always match and have problems with decimals. I have estimated swordfish demand models using total weights but not in dressed weights. It may not be a simple matter to estimate directly an inverse or quantity dependent single equation for swordfish--we have imports and substitute species affecting the ex-vessel prices.
If you can obtain the buyer or processor/wholesale data by market category, you may have enough observations to estimate a very simple equation--price as a function of quantity landed and disposable income (shold try per capita quantities and ). Also, use the producer price index to deflate the ex-vessele price--availab le for fish and shellfish from BLS. Also, for really simple, try population rather than income.
You Actually should be considering a system of equations, but consider seemingly unrelated regression in which you have an inverse demand for each product--if you can obtain data by category. For simple starters, however, just do an OLS and see what you get.
The notion that prices vary by size or quality is well known and has been documented for many species; it is very likely true for swordfish--particularly given the boycott of several years agol
A synthetic inverse demand model typically works quite well but you usually cannot get more than 24 demand equations per system of equations--unless running on main frame!