JOEL - According to the Church Handbook(#1):

"When several brethren participate in an ordinance or blessing, each one places his right hand lightly on the person's head (or under the baby being blessed) and his left hand on the shoulder of the brother to his left. Large numbers of brethren are discouraged from participating in a single ordinance or blessing."(page 22)
"When blessing a baby, Melchizedek Priesthood holders gather in a circle and place their hands under the baby." (page 24)

From what I know it doesn't really matter if the one voicing the blessing uses both hands or one hand. I have seen it done both ways with no complaints. However, I don't know any father(including myself) who would keep only one hand under his own baby.
Doing this is mostly a matter of convenience so that all those in the circle can reach the recipient's head with their right hand. It depends on how many there are and how big they are. A blessing is not invalid if one brother doesn't happen to have his left hand on the shoulder of the person next to him; but doing this represents a sense of order, unity and an unbroken circle of priesthood power for the bennefit of the recipient. What is most important in giving a blessing is the priesthood authority and that it is done in the name of Jesus Christ.
The Church Handbook(#1, p. 23) states that even a handicapped person with no arms can still perform the ordinance.

"Persons who have physical disabilities such as the loss of one or both arms, paraplegia, quadriplegia, or hearing impairment may perform and receive ordinances and blessings. Leaders make the necessary arrangements for these persons to participate in a way that their disabilities allow."