Must the questioner postpone the obligatory Hajj this year to preserve his family's stability, or should he proceed with the Hajj this year, knowing that his wife will not be able to perform Hajj, for fear that a health impediment or death may prevent him from performing the obligation in the future?

If you are unable to perform Hajj, then Hajj is not obligatory upon you with the free campaign, and there is no blame upon you for waiting to perform Hajj with your wife in another year. This is because Hajj is not made obligatory by the effort of another, nor does a person become capable by that means. If you are able to convince your wife to let you go alone without causing discord, then proceed with Hajj. Otherwise, wait until you can perform Hajj with her.