Hopefully both of these devices will work. My life was a lot easier before I started hanging out on these forums, and trying to learn. Don't get me wrong, you guys are great, but sometimes ignorance is bliss....
No, it isn't, unless you consider "bliss" as having to replace batteries sooner than optimal. ;)
You may wish to consider adding a solar panel and charge controller or buying a power supply since there are reasons to get charging voltage to around 15 V, at times. That is considered an "equalization" procedure and, as batteries age, it will extend the capacity of your batteries. I don't know what US battery specifies as a routine charge voltage but the 6V batteries I've dealt with all liked a diet of 14.8 V or higher.
Both of the chargers you are buying will not harm your batteries. Floating them at a constant lower voltage is the best care you can give them.