The verb tense changes to the conditional; the conditional is a tense that signifies "what if?". We use the conditional to express hypothetical situations that we have not yet acted on or do not plan to act on. The conditional is sometimes also associated with "wishing" as opposed to actually "doing."
This shift into the conditional signifies Prufrock falling further and further into inaction; ironically, though Prufrock states that he is "not Prince Hamlet, nor was meant to be" (111), his most prominent characteristic is indecisiveness and an inability to act, which is also Hamlet's tragic flaw. The conditional tense indicates that Prufrock is sitting back wishing and thinking rather than being an active participant in his life, and as a result he grows older without gaining any new experiences. He imagines what these experiences might be like, such as when he imagines riding with the mermaids at the end of the poem, but ultimately he is unable to be a part of them, and his sudden shift to a rhetoric of "wishing" is a key signifier of that fact.