Short answer:
No. They have to move in order to have their hazard limit reduced.
Explanation:
Both Crept Along Carefully and Going Ever Under Dark have similar hazard-limit-reducing effects; for example, consider Going Ever Under Dark:
The “if” clause indicates that both the region maximum and the hazard limit reduction are only applied when the delineated condition is met. In other words, the company needs to be moving with region movement to have its hazard limit reduced, and thus a non-moving company’s hazard limit will not be affected.Playable on a company during the organization phase. The company cannot use starter movement. In addition, if they move with region movement, they are limited in all cases to 3 regions maximum and their hazard limit is reduced by one (to a minimum of two). Discard this card from play and make a roll to attempt to cancel an attack against them by an opponent's company. If the roll plus the number of scouts in the company is greater than 7, the attack is canceled. Discard during your organization phase if you choose. Cannot be duplicated on a given company.