Cognitive radio (CR) technologies have long been studied and continue to attract attention for their potential to enhance wireless spectrum sharing and utilization. In CR ad hoc wireless networks (CRAHWNs), unlicensed secondary nodes (SNs) are equipped with CR transceivers capable of continuously scanning for unoccupied wireless channels. This scanning process is managed through channel-hopping (CH) rendezvous schemes, which assign CH sequences to SNs, enabling dynamic control of frequency-hopping patterns used by their CR transceivers. Traditional CH schemes operate under “global” labeling, where all SNs share an identical mapping between logical channels in their CH sequences and the transmission/reception frequencies utilized by their CR transceivers. However, when SNs operate with differing channel-to-frequency mappings—arising from regional variations or restricted access to a common frequency set—rendezvous attempts fail, preventing data exchange. Despite its importance, the development of CH sequences capable of supporting “autonomous” labeling, enabling SNs with diverse channel-to-frequency mappings to achieve successful rendezvous, remains unexplored. This paper introduces a novel class of asynchronous “universal-label” CH sequences designed to seamlessly adapt to both global and autonomous labeling frameworks. Performance evaluations demonstrate that the proposed sequences achieve an optimal balance of essential properties. These advancements enable efficient spectrum sharing and utilization in CRAHWNs, even under challenging autonomous labeling scenarios.