1. Shaun Alexander
2. Marshawn Lynch
3. Curt Warner
4. Ricky Watters/Mack Strong
5. Chris Warren/John L. Williams
My list is both with and without the FB position. The OP's criteria said without, and thus Watters and Warren make the list. But to me, having a list without including fullbacks leaves off a couple of the best backs we've seen in the Seahawks uniform.
The first three are easy. Their position relative to one another is probably debatable, but their status as the top three is hard to argue against. They are a cut above the rest, and by a good bit.
Shaun Alexander suffers from public perception based on a year running with a broken foot. For years before that, I can't recall ever hearing the "soft" label about him. All we ever heard was how smooth he was, and how long that streak of at least one run of 10+ yards per game had become. Remember that? Every Sunday it was a given that Alexander was going to get his yards, and with it at least one decent run to extend that streak. Each run may have been inconsistent in that he gained yardage in a very Barry Sanders-esque fasion: sometimes a loss of two, sometimes a gain of 35. But while that aspect of his game may have been inconsistent, what was very consistent was his ability to get yardage by the time the game was done. You could not contain him; you could only postpone the yardage and try to mitigate the damage. I think if he'd have been IR'ed in '06 and allowed to heal completely, he'd have been a very different -- and much more productive -- back for years longer than he was, and our perception of him would be far different than it is.
Marshawn Lynch, on the other hand, benefits from public perception based on his running style, and largely influenced by one single play. While he is a great runner, and could well end up on top of the pile as the greatest Seahawks running back ever, he is a bit overrated when it comes to public perception. Everyone makes the comparison between the '05 and '13 offensive line, and uses that as an excuse for Alexander's dominance, but the '13 team wasn't that bad at run blocking. It was pass protection they were dismal at much of the time. And Lynch often runs straight into contact rather than avoiding it. While he has had some amazing plays juking opposing players out of their shoes, he often bulldozes straight into the defense and takes the hard yards, counting on blown tackles to add to his totals, instead of stepping around contact like Alexander did. If he had the '05 line in front of him, he'd almost certainly get more yards than behind the '13 line. But he may not get the yards people assume because of his running style. Still, he has the potential to eclipse Alexander if he gets the yards and touchdowns over the next few years. If their numbers are close, Lynch gets the nod in my opinion. He's not there yet, but he could get there if we don't move on before it happens.
Curt Warner suffers from the difference between potential and actual production. While he may have been the most talented back the Seahawks have ever seen, we'll never know if he was the best. He didn't put up the consistent, long-term numbers to make that case. That's just the way it is. Still, he's undeniably better than the rest of the guys on the list, and will be for quite some time. It'll take another long and accolade-filled career for him to be bumped into fourth place by another Seahawks back.