Yep, there is... and it's pretty easy too. Although, you would need to cut off the plugs for each light and then wire a new one. Why not just use an extension cord that will accept two plugs?
Yeah, you can, just get a replacement cord at lowes with the cords already cut off and wires exposed.
Cut the ends off the UV and basking bulbs, wire positive to positive (white) and negative to negative (black) and if there is no ground needed, cut it off.
Cut the ends off the UV bulb cord and cut the ends off the basking bulb cord, expose the wires.
Connect the basking bulb wire positive and the UV wire positive to the positive (white) on the replacement cord.
Then
Connect the basking bulb wire negative and the UV wire negative to the negative (black) on the replacement cord)
Cut the green wire off, It's the ground, you don't need it for this.
If you have a solder gun, solder the wires together, if you don't just make sure they are good and wired together.
Get some shrink tube to cover the exposed wires.
If you are going to cut and splice wires, MAKE SURE that the new wire will handle the amperage of all the fixtures you will splice. Too little wire and you will have a fire. Best to go with a surge protector. One button and everything goes off at one time.
If you were to run both wires to a box with a dimmer switch, hooking your basking bulb to the dimmer, you can come out the box with one cord to provide power to both fixtures. Having a dimmer on your basking bulb allows you to fine tune the basking temp.