It's technically possible, but there are major catches. Wildberries and Ozon keep logistics in their own hands for a reason - the marketplace terms usually don't let you pick up goods from the warehouse and arrange delivery yourself, and that would violate your agreement. Even if you manage it technically, you'd have to register as a sole proprietor and get a transport company license if you're using a third party, or register as a carrier yourself with all the insurance and reporting that comes with it.
It's easier to just accept that the marketplace commission is already built into your business model as an expense. Instead of fighting the system, maybe check if it makes sense to lower prices for direct sales through your own website or social media - there you'd only have commission on payments, and you could arrange delivery directly with a courier service more easily?