You can still use AuthNet Accept.js for partial charge if you want to but any further charges with the same authorization will have to be done form within your Authnet account.
Basically say you have an order for $100 and shipping is TBD so you can auth & capture $100 at time of order placement. When you know how much you will charge for shipping you go to your Authnet account find the authorization for the transaction and run another charge on it.
But you cannot do this from XC, it has to be done from Authnet.
If you do not want to use XPayments then you have to find another payment processor and not Authnet Accept.js. I am not sure which one will work like this without XPaymetns. Check the payment gateways XC supports.