The lexicanum site is down, so my research is not as complete as it could be, especially on the equipment front, but here goes.
Orks are tough. As in, a gun which cuts humans in half warms them slightly. It takes rapidfire RPGs, molecular shuriken, swarms of ultra strong scythe bugs, or ANTI ARMOR WEAPONRY just to kill them.
You got to remember that Snikrot can take down Space Marines, who are the greatest warriors of the Imperium. And Snikrot would probably survive a spear lodged in his chest, I doubt Ajax could survive a stikkbomb.
Snikrot. He's bigger and stronger(maybe? bigger at least) than Ajax, and Ajax's weapons would probably just get stuck in him ineffectually.
If Ajax hits you, you're going to feel it a lot more than any other person. Ajax chucks around boulders and can fight several people at a time without sustaining injury. Furthermore, the ability of the Orks to fight on despite injury stems from the Waagh, which is a psychic field generated by the presence of other Orks. Since Snikrot is fighting without assistance from other Orks, this would mean no Waagh.
a spear is almost completely useless against an ork, as they don't feel pain, and have skin comparable to armor. And they wear armor made from the skin of Squigs, which are nonsentient cousins of orkkind and thus have similarly tough skin.
Ajax has no viable way of doing any real damage.
Ajax doesn't have the weapons to even pierce the skin, even then only with a terribly lucky blow.
I'm afraid I haven't been able to find reference to Orks having skin like armor. I'm going to have to ask you to back that up with a link.
Heck, snikrot can probably heal faster than mere swords can hurt him.
From my reseach, the Orks do have more effective healing than humans, but nothing like that. The example that I found was that a dismembered limb could be rejoined with the Ork if they were held is statis for a while, but nothing that would be any use in a battle. It could be accelerated somewhat by the presence of the Waagh (if it were present, which it is not here), but even if it were, it would still act too slowly to be any use.
You don't usually use swords for stabbing, you use them for slashing.
You use different swords for different things. Indeed, one of the strengths of the Roman army was that most of the soldiers were equipped with Gladiuses, which could be used for both slashing and stabbing.