In the US, we often use "swerving" to describe a car that appears to be driven by a drunk driver. As in, "That driver must be drunk; he's swerving left and right." Since you mentioned the drunk cyclist not being able to follow a straight line, I think swerving works. But if you want to describe how a drunk cyclist is unbalanced and in danger of toppling over, then I think wobbling is a better choice of word.