Tether USDT raw transaction unsigned
The only omni-specific thing in Omni/Tether txs is the OP RETURN, and a small dust output to the address you are sending the funds to. Both of these seem to check out in your tx (I'm assuming you're sending to 1KH34S5mAmgAzu3mJAqrS3wjP15qYKZQXx).

You should be able to just use the regular Bitcoind signing functionality (or whatever library you are using's wrapper of it). They don't require any special signatures.