If the DM allows the pixies, it works as described.
If the DM permits the pixies, this is quite straightforward. The pixies can cast polymorph, and since they obey your commands, you can tell them who to polymorph into what, according to the limitations provided in the description of polymorph, as you describe in your question. However, there is an important caveat here:
The DM decides what creatures are conjured.
This is addressed in the Sage Advice Compendium:
When you cast a spell like conjure woodland beings, does the spellcaster or the DM choose the creatures that are conjured?
Some spells of this sort specify that the spellcaster chooses the creature conjured. Other spells of this sort let the spellcaster choose from among several broad options.
The design intent for options like these is that the spellcaster chooses one of them, and then the DM decides what creatures appear that fit the chosen option. A spellcaster can certainly express a preference for what creatures shows up, but it’s up to the DM to determine if they do. The DM will often choose creatures that are appropriate for the campaign and that will be fun to introduce in a scene.
So for this to work, the DM has to permit the summoning of the pixies. Every DM I have tried this with has not allowed this because of how obscenely powerful it is, and I've forbidden it before in my own games. So the important thing here is:
Ask your DM about this before you try it in play.
This is the sort of unbalancing loop hole that DMs really like to be briefed on before they come up in the game. Again, this combo is obscenely powerful for what it costs, and it can be a source of sore feelings when it is a surprise. Once the party planned their assault of a chapter villain around summoning pixies and polymorphing the whole party into a gang of giant apes, while assuming that the caster was allowed to choose. They didn't tell me, the DM, of their plans, and had never used conjure woodland beings before. When the moment came, the druid declared:
I use conjure woodland beings to summon eight pixies!
I took the wind out of their sails when I informed them that they didn't get to pick, and I would be choosing randomly which sort of creature appeared:
You don't get to choose, it's up to me, and I like to determine it randomly. Do you still want to cast the spell, or do you want to take a mulligan?
The druid decided to take the one in four chance for pixies, and ended up with a pack of rabid blink dogs. The dogs still helped, but all of their eggs were in the basket of giant apes, and the druid was pretty salty about the plan not working out, and improvising their way through the fight made it far more difficult than they were expecting.