[mothered]

The company I'm currently SEing doesn't give prepaid shipping labels, or state anywhere that you are required to have a tracking number, so I told them I used the cheapest USPS option which didn't come with tracking.

If they don't provide shipping labels nor tracking numbers and do not request to do so anywhere In their terms (Inclusive of nominated carriers), then you're free to use your choice of shipping.

I believe you'll be fine.