The plugin does a 301 permanent redirect in the .htaccess
As far as I know the .htaccess redirect is the fastest way of redirecting. Besides that, it is only used when the site is accessed over http. I’ve never actually seen this slow a site down.
The mixed content fixer replaces http urls to https
I’ve done some tests with it on my own site. With a source consisting of about 60.000 characters, the delay caused by the mixed content fixer is about 0.00188 seconds, which I think is pretty good. But you can of course disable the mixed content fixer in the settings. You would then have to fix your mixed content manually. If you don’t have a lot of pages, and your theme and plugins are well built, this won’t be much work.