I agree with those who say put in the new battery. You can keep the old one around for a backup for a while, and then just let it gather dust waiting to be taken in as a core for a future battery purchase. I have much experience with lead acid batteries, and I do not recommend most float chargers / battery tenders, etc. Constantly keeping a battery on float charge WILL shorten its life. On the maintenance free batteries it can cause a very slight outgassing which will lower the level of electrolyte, reducing capacity. And with the plastic case batteries of today, they can sit on any surface, and dry is better. The old hard rubber cases could deteriorate from sitting on damp concrete. And if you are going to store a battery, cooler is better, as self discharge is less at lower temperatures. It is not good for a lead acid battery to be stored where it is above 85° F.

Good luck.