In Sorry can I split a 7 move card to a single pawn and move it only 2?
No, you cannot use the 7 card if you lack a man (or pair of men) that can move a total of 7 spaces.

In the scenario you provided, you have one man that can move 2 spaces, and all three other men can move 0 spaces (whether this is as a result of being on Start or being in Home is actually irrelevant, as the only three cards that can move a man out of Start are 1, 2, and SORRY!). Since you cannot split the 7 card with any of the three men that can move 0 spaces, your only other option would be to move the remaining man 7 spaces, which also cannot be done. Therefore, you forfeit that movement (and thus, the turn).

It's worth noting that the only 4 cards that could be used in the exact scenario you provided (three men in home, last man 2 away) are a 1, a 2, a 4, and a 10 (forces your man one space back). Any other card would automatically cause a forfeited move because you cannot perform the movements on the card.