My first was this way, so I learned to do everything one handed (including typing!) from the get-go ... it was only with later kids that I realized constant carrying wasn't To Be Assumed ;). If you have a snuggler, you have a snuggler ... it's just different with each kid. And anything you don't give him now that he needs (and at this young especially, babies can't "want," they only have needs), he will keep needing, and it will only be harder (for him/you/his future partner) to access that infant-emotional-space to fill the need later, especially if he finds it is not "safe" to ask/want/need it at this young of an age ...
There are lots of slings on the market. I am small-shouldered and even the "smalls" didn't fit right, but the Moby wrap I borrowed (from a much broader-shouldered friend) was fabulous, especially since it distributes weight over BOTH shoulders and is stretchy.
As soon as he is big enough to sit up by himself, you can carry him on your back ... and if the housework etc. slide for the next 5 months, please remember you are making his and your and your husband's life easier for the next rest-of-baby's-life ... it is a short (if painful) sacrifice.
Two parting hints: I still wince to my environmental self, but it is a VERY good idea to have a stash of paper plates and cups on hand, for those days (it was about once a month for me) when the dishes just weren't going to happen at all. And second, a lot of "table" work (eg, laundry, reading mail) can be done on the floor, with baby laid across your lap or, when he is a little more independent, on the floor next to you (this gives your back a huge break!).