Don't just remove the blood line, but the whole skin side. I do this:

Fillet the side of the cat per usual.

Now, look at the fillet, skin side up (skin should be removed by now), see that seam going from tail to head? Split that seam, all the way from end to end.

Cut those two pieces into about 3-5" pieces top to bottom.

Now to remove the taste. Put the pieces skin side down, thick part facing you, see where the fat changes into good meat? You need to press that fillet down lightly, using a normal or electric knife, fillet that part off. On a big cat you may need to remove 3/16-1/4" of meat to get rid of the fat. I use this technique even on smaller channels, just don't have to remove much, more of a shaving except the chunk right where you split the fillet. Smaller fish is more of a wedge cut instead of actually filleting the side off.

In the end it seems you're wasting a bunch of meat, but you are creating magic. That resultant fillet of fish is delicious.

I have family and friends that swear they can't eat anything other than crappie or like tasting fish... they have eaten a meal of my cat not knowing the difference other than mentioning the size/shape. I repeatedly ask, "how's the fish".... then tell them. 100% cat. Now, I have plenty of folks that love cat, if I clean it.