Oh!
Well, I must confess I have not seen a carb inlet valve that looks like that one. The parts page doesn't show it either. The only ones I've ever run across had the hanger head machined right into the metal of the valve. Simple.
Not sure why it's been made more complicated with that plastic head but all I can do is tell you what I would try.
Obviously, the head or cap or button holds the hanger to the valve. I can't tell, from your photo, if the hanger wire slips under the head or, has to be "captured" by the head as you insert it into the metal.
If it's the latter, then you have to make sure that the orientation of the hanger is correct for smooth movement of the valve when it's hooked to the float and installed in the fuel inlet passage.
It actually may not matter but I would consider it before assembly.
I take it, from you even asking the question, that sucker is hard going on. And, you're right, you should avoid boogering up those little guide fins on the valve.
But I don't think it would hurt to give it a tap or two to get it to go in. You could put the cap in the fridge for a time to shrink it a bit and then lube it with Vaseline or WD 40.
Use a plastic faced hammer or maybe a block of wood to tap on the cap head ONLY. You're probably going to have to hold it in your fingers for this little operation to keep from damaging the valve guide fins.
Then.....hold your tongue just right.
I wish you luck. It looks like it's going to be a pain.
Let us know how you get it in (you WILL if you keep trying).