It's okay to use it without the base, in fact that's what I was going to suggest! I would have it installed by a certified car seat installer. My daughter's is without the base, it fits so much better, especially when it's rear facing. To my knoweledge it is not any less safe without the base. Plus, you have to consider that it's not particularly safe when the driver of the car is uncomfortable and can't move easily either! You can go to the fire station and they will do it for free. I notice a BIG difference when we install the car seat and when they install it. When a "pro" does it is so much tighter, it's crazy.
*I wanted to add that you will definitely have to look at your state laws, but it is not illegal to use your seat without a base. It's not as easy or convenient, but not illegal. Most people use the base, but I believe they are designed to be used with or without for people who don't want to or can't financially afford the base. If you feel like you don't want the carrier option, you can just go ahead and buy a convertible car seat and have it rear facing. You can get ones that are for newborns (like 6lbs and up) through 30 or 50lbs. Honestly, go talk to the firefighters and they can help guide you if you don't have another resource. They install seats all day in all types of cars.
*I also wanted to add that I didn't really clearly read your question...my answer was more talking about a convertible car seat, not a carrier. I would recommend using the base just for ease of convenience b/c otherwise you would probably just keep it installed as opposed to reinstalling it every time you put the baby in the car. Michelle did have a good point about putting it in the middle, that will save on space for sure.