Because you probably want to logrotate a number of OS logs on each VM, it's probably easier and cleaner to just install logrotate. That's definitely my recommended solution.
Regarding the 10 logrotates vs. 1 logrotate resource issue, I don't think that's something to be concerned about. That's WAY premature optimization. Do it the correct way first, and then make it faster if necessary.
Logrotate will run once per day; on my system it takes about 0.002 seconds to run. It will take a lot longer the first time, but after that your resource hit will be next to nothing.
You can even make it better by staggering the time your /etc/cron.daily scripts execute -- so not all the virtual machines execute at the same time.
(And since whatever slows your system down will be the actual moving/truncating/renaming/gziping/etc. of the logs, and that will happen with one or 10 logrotate processes -- it's another reason to go with one logrotate per VM. The overhead for logrotate itself is so minimal it's lost in the noise.)