[Legbreaker]

Yes, once the majority of current naval shipping was on the bottom, the military would probably start scrounging around for whatever was available. However, with most of the older vessels being little more than rusted out hulks, it may not be worth the time and effort to conduct major works. It's likely that any modifications/upgrades would consist of little more than slapping a few anti-air guns and missiles onto existing civilian craft.

By Christmas 1997 the world is in bad shape. Nukes were first used by the Soviets on the 9th of July 1997 (in both China and Europe - both 1.0 and 2.0/2.2). This would undoubtedly have caused world wide panic as the reports of nuclear escalation rolled in across the news services. Many skilled workers, required to operate the shipyards, will have "run for the hills". Some would trickle back in the coming months, but never enough to satisfy demand and even keep up with repairs on existing warships.

And then there was the escalation.
Version 2.0/2.2 states:

In the west, NATO air units begin making deep nuclear strikes against communication hubs in Czechoslovakia and Poland in an attempt to slow the Warsaw Pad advance. The Pact responds with similar strikes against German industrial targets and major port cities. NATO's theater nuclear missiles are launched against an array of industrial targets and port cities in the western Soviet Union. Throughout October the exchanges continue, escalating gradually. Fearful of a general strategic exchange, neither side targets the landbased ICBMs of the other, or launches so many warheads at once as to risk convincing the other side that an all-out attack is in progress. Neither side wishes to cross the threshold to nuclear oblivion in one bold step, and so they inch across it, never quite knowing they have done so until after the fact.
First, military targets are hit (including the first decapitating strikes at US targets). Then Industrial targets clearly vital to the war effort, followed by economic targets of military importance (transportation and communication, oil fields and refineries). Then major industrial and oil centers in neutral nations are targeted, to prevent their possible use by the other side. Numerous warheads are aimed at logistical stockpiles and command-control centers of the armies in the field. The civilian political command structure is first decimated, then eliminated (almost by accident In some cases). The exchanges continue, fitfully and irregularly, through November and then gradually peter out.

Version 1.0 has:

In the west, NATO air units began making deep nuclear strikes against communication hubs in Czechoslovakia and Byelorussia in an attempt to slow the Warsaw Pact advance. The Pact responded with similar strikes against German industrial targets and major port cities. NATO's theater nuclear missiles were launched against an array of industrial targets and port cities in
the western Soviet Union. Throughout October the exchanges continued, escalating gradually. Fearful of a general strategic exchange, neither side targeted on the land-based ICBM's of the other, or launched so many warheads at once as to risk convincing the other side that an all-out attack was in progress. Neither side wished to cross the threshhold to nuclear oblivion in one bold step, and so they inched across it, never quite knowing they had done it until after the fact.
First, military targets were hit. Then industrial targets clearly vital to the war effort. Then economic targets of military importance. Then transportation and communication, oil fields and refineries. Then major industrial and oil centers in neutral nations, to prevent their possible use by the other side. Numerous warheads were aimed at logistical stockpiles and command control
centers of the armies in the field. Almost accidentally, the civilian political command structure was first decimated, then eliminated. The exchange continued, fitfully and irregularly, through November and early December, and then gradually petered out.

As we can see both are very similar. The only significant difference is that 2.0/2.2 specifically states attacks were made against US targets.
Howling Wilderness has this:

With the first use of tactical nuclear weapons in September...

This has to be a typo as BOTH histories state nukes were first used on the 9th of July. My suggestion is that this should have read "strategic" rather than "tactical" due to the information quoted above about the escalation. By reading over the preceding several paragraphs (see the books), it seems the first long range strikes began in September.

While not specifically stated anywhere in V1.0, it is therefore not unreasonable to assume some limited strikes were made against US soil prior to the 28th of November 1997. These limited, even surgical attacks would have inflicted damage far beyond their actual physical effects by driving away people from potential target areas and keeping them away.

Bear in mind too that the last fleet of US/NATO warships were not sunk until approximately 3 weeks (sometime in June 1997) before the first nuke was used anywhere in the world. It is doubtful, as mentioned here http://forum.juhlin.com/showthread.php?t=2462 that there'd have been any significant headway made into even organising a search for potential warships to rebuild before the panic really set in.

One more thing. With no effective enemy naval forces anywhere in the world, what would be the driving force behind such a huge undertaking? Where is the benefit versus cost?