I imagine (and describe some of) the fighters to be using edged weapons exclusively, yes, namely regular swords, daggers, and a few axes. The professional soldiers will be moderately armoured, as they've got their gear around, and the others are chiefly unarmoured; most of the pirates are described as having leather chestpieces, whilst others are also unarmoured, so yeah, leather and some mail sounds fitting for the armoured blokes. And yes, the fight is very crowded, as all those people are on the cog's deck, and the pirates attempt to "push back" and separate the defenders as much as possible, given that some of the defenders are better-equipped.
(Let's ignore the probability of that sort of equipment being used when caravels were widespread.)
Exactly the thought of blood absorption by clothing is what makes me conflicted about the subject. In a previous swordfight with only a dozen or so guys on each side, where everyone had manoeuvring ground and the numbers were almost equal, I didn't really think about this at all. But now, because we're talking about lots of corpses on the deck,
and choppy wounds to major blood vessels, I don't know how it'd look.
Sure, a severed artery would lead to exsanguination, but I doubt that the blood would gush out with enough momentum to spill all over the place, and I also doubt that it'd spurt sideways, creating a bigger mess, instead of just flowing down the victim's body.
But then again, I've never experimented with cutting living people's arteries, so I wouldn't know for certain.
Maybe a reasonable conclusion would be a very filthy deck, but with a lot of the blood still on the corpses, and only a little spatter here and there on combatants, each one being more affected from his own personal wounds than from any potential outside source? Except those unscathed, of course.