Would a conventional Cold War naval campaign stay non-nuclear?

Would a 1986 NATO-Soviet war inevitably escalate to nuclear weapons?

Not necessarily or immediately; both sides have strong reasons to preserve deterrence without triggering retaliation and contaminating their own operational routes.

Leaders must appear willing to use nuclear weapons for deterrence to remain credible, yet the first detonation invites retaliation and a much wider exchange. Tactical weapons contaminate terrain, water, and the routes that advancing armies need to use. Later replacement formations may also be less well protected than the first-line units equipped for a nuclear environment. The incentive to employ such weapons can therefore decline as a conventional campaign continues, even while threats remain politically necessary. Attacks on national territory or strategic assets remain possible escalation triggers, so the scenario is plausible rather than guaranteed to stay conventional.