I'd say no swing too!
Unless the recommendations have changed, I thought that things like exersaucers were viewed as really bad for their development?? Because they are upright before they really should be and it can delay walking. I'd encourage you to have a read online about it before you decide to buy one.
Yes, I would get my emails etc done during y time - any household jobs that I could do with him up though, I would. Pop him in the highchair in the kitchen while cooking, take him shopping with me and chat away whilst showing him all the things you are buying. Etc!
I heard on the radio something that has stayed with me -don't know if it holds much water - that a child's life chances to age 30 are determined by the number of words he or she has spoken to them up to a certain age (3, I think). So take every opportunity to be 'present' with him, even if you are physically getting something else done.