Which rear cog should I remove if I want to add a 26 for climbing? I have an old road bike with 53-39 rings and 13-23 cassette. Although it's generally flat in my area, I like to get to the top of these hills where they put the radio antennas (without dying). Max slope on these is 15%, average 8% and I suffer a lot.

I have spare cogs, rear mech is Shimano RX100 and thought I can fit a 26T in the cassette Which cog should I remove from my current setup (13-14-15-16-17-19-21-23)? I guess either the 16, the 21 or the 23?

I'm already assuming body fitness can be improved ;) Thanks!

Edit: here are the gear ratios
http://gears.mtbcrosscountry.com/#700c/23I61I3909X700c/23I61I193X700c/23I61I15271X700c/23I61I15275



Report back (edit 2): I set 13-14-15-16-18-21-23-28 today. I just realized I have a 24 I could swap for the 23 to make a fairer gap, and I still have the 26 available. There is room for the 28T and didn't touch the B-screw. For now, it shifts fine standing, I have still to ride test it. I'll get back.



Conclusion - edit 3 :)
Went for a small ride with climb included. Setup is still very close to what it was, introducing the 18 as Grigory said and leaving room for a life-saving 28 (thanks Criggie for the tip).

Shifting is good, I didn't notice much change, but as ChrisH and Criggie pointed out, it probably is a bit irregular on the new cogs. So I will eventually look for a complete cassette.
Anyway, many thanks to all. I'll accept Grigory's answer as it addresses the original question with a better alternative to do what I intended.
The answer in terms of ratios might not be the same as the answer in terms of being able to shift. Taking out the 16 would be reasonable but then the shift ramps and pickup teeth wouldn't align. This issue will occur going from the 23 to the 26 whatever you remove. 

You've got 8 gears in the back so I assume you've got indexed shifting. If you're using friction shifters it's not an issue as you can overshift then back it off.

Further reading from Sheldon Brown