Well, there isn't quite enough information here, but I'll take a stab. First, if your 6500 is the owner of all your other vlans, what is stopping you from creating your new vlan on the 6500, and trunking vlan 1, 35, and this new vlan. Then your 4900 will know about the new vlan and you can assign all of its ports as necessary, without making this more complicated than it needs to be.
If for some reason the above scenario is impossible (ie there is some requirement that I'm not privy too) and this new subnet MUST stay on the new device, then you'll need to skip trunking and make sure each switch has an interface in the proper network (vlan 35). You'll want to create this new vlan on the 4948, and turn up a routing protocol to exchange the network information with the 6500. This way your 6500 will have a neighbor relationship with the 4948 via 10.35.0.3 and will be told about the new network, and will route as necessary. Just make sure your 4948 is getting all of the desired routes in the other direction. If this is some kind of isolated VLAN, you may want to use a distribute list or ACL to protect that network as you see fit.
Hope this helps...best I can do with the information you provided.