So you are saying with the proper precautions code will allow you to do this with 10-3 wires to another set of 10-3 Wires going to a Dryer receptacle! Also is the standard Wire Capps rated for 10-3 wires.

Install them in a junction box and use red wire nuts. Fine for 10/3. Look inside the box, to see how many 10 AWG wires can be installed. A B122A Carlon nail on new work box-22.5 ci.- allows 9#10AWG conductors.