The warlock made a pact with a powerful shapeshifter or beast god, like Malar of the Forgotten Realms. This pact concentrates of attaining the ability to change into various beasts. This is much like the Moon druid subclass in many cases, but overall, this subclass is less powerful in most regards.
At 1st level you get the shapeshifter subtype and can grow either claws, fangs or a horn as a bonus action. Claws go with d4 finesse and light, the bite with d6 finesse and the horn with d8. You have proficiency with all kind of natural attacks. Additionally your beasty nature allows you to roll animal handling and charisma checks with advantage, as long as you interact with beasts.
Your pact spells could be:
1st – Beast Bond (EE Player Guide), Longstrider
2nd – Pass without Trace, Moonbeam
3rd – Bestow Curse, Nondetection
4th – Locate Creature, Greater Invisibility
5th – Commune with Nature, Reincarnate
At 3rd level you have to take a new form of a pact boon, Pact of the Beast. This will be your wildshape-kinda feature, even though it is more restricted. You can only use it once per short rest and have to spend a spell slot to do so. Otherwise it works like wildshape, even though you can use it as a bonus action (but not spend spell slots to heal yourself). And even though you should name it differently, you also get the Circle Forms.
At 6th you get the Primal Strike like a Moon Druid.
At 10th level when you’re in beastform, you have resistance to non-silvered, non-magical weapons to increase the unholiness of the shapeshifting nature. Your natural weapons also count as silvered.
At 14th level you can use your form of wild shape as often as you want, as long you have spell slots. You can even change your shape when you’re still in another.
You can add some druidic spells as invocations, like speak with animals at-will, conjure animals once per day by spending a spell slot, etc. I would choose those, who would make your warlock more like a leader of a pack or an animal master.
Since Wild Shape levels with the character, the other features aren’t too impressive, but it should be a good way to embrace the beast while remaining a warlock in all other aspects. Polymorph wasn’t added for a reason, since there is already an Eldritch Invocation for this and it should be only be usable once per day, since this spell packs a lot of power.