You are stripping speaker cable correct? Is it CI-PRO or some other version of Monster Cable? The rip cord inside CI-PRO is one of the few that actually will cut the housing cleanly if you want to do it that way.
The first wire stripper you are showing is more of an electrical heavy duty stripper. It is better than the second item, but is still not nimble enough for what you are looking to do. You need a gentle touch, and that thing is a sledgehammer!
The second tool is designed for stripping coaxial cable.
Not sure where you are located, but I picked up my Ideal wire strippers from my local Home Depot store. They had different sizes, and different choices. There are also Klein wire strippers. Not sure where you are located, but I wouldn't think you are so limited.
If those really are your choices, get some electricians scissors as they will do the job equally well. The tool I listed above - you don't actually 'strip' the housing. You use the wire cutters in the center and press the wire into it, then spin the strippers around it a bit. The housing is scored/cut and then just slides right off.
Good electricians scissors should be available to you and will do this equally as well...
Image of what I'm talking about: