At 165, you don't need a huge spring rate, so there are more options. ZX14 is pretty stiff, as I recall, and might be a bit much for your weight and weight of SV. Check the rates on ZX10 and ZX6/636. Don't know them off hand. From what I've seen, the ZX series shocks require no cutting of anything, but they also usually sell for more than the GSXR shocks, so depends how cheaply you're looking to get it done.
I weigh about the same as you, and I went with a GSXR 600 shock. Its spring isn't as stiff as a 1000 spring, but published spring rates put it in the right range for our body weight and bike. The 1000 shock also requires you to cut your battery box and find a shorter battery. Benefit of the 600 shock is that you only have to cut into your toolbox, but the kit will fit in the trunk, anyway. For a budget, it's also a good fit. I picked up an 08 shock for $18 plus $10 shipping on ebay. Also required a raising link, since the shock install dropped the rear end 1/2", but that was only another $18 shipped from ebay. All in all, I'm happy with the change.
I weigh about the same as you, and I went with a GSXR 600 shock. Its spring isn't as stiff as a 1000 spring, but published spring rates put it in the right range for our body weight and bike. The 1000 shock also requires you to cut your battery box and find a shorter battery. Benefit of the 600 shock is that you only have to cut into your toolbox, but the kit will fit in the trunk, anyway. For a budget, it's also a good fit. I picked up an 08 shock for $18 plus $10 shipping on ebay. Also required a raising link, since the shock install dropped the rear end 1/2", but that was only another $18 shipped from ebay. All in all, I'm happy with the change.
