Vehicular Ad-hoc Networks (VANETs) are an essential part of the Intelligent Transportation System (ITS). VANETs promise to offer drivers and passengers safety, traffic efficiency, and infotainment services. To this end, VANETs require vehicles to periodically broadcast unencrypted beacon messages that contain position, velocity, timestamp, and identity. Consequently, VANETs naturally expose users' identities and locations, facilitating tracking by an adversary. To address VANETs location privacy issues, researchers have proposed different pseudonym-based privacy-preserving techniques in the literature. One of the techniques is pseudonym swap. In pseudonym swap techniques, vehicles exchange pseudonyms with each other hence fewer pseudonyms for each vehicle since vehicles can reuse pseudonyms. However, existing pseudonym swap-based schemes either exchange pseudonyms via Roadside Units (RSUs) or ignore VANETs' security requirements by not informing the Certification Authority of the exchanges. Hence, they suffer from high RSUs deployment costs, inflexibility to location privacy preservation, unaccountability, and repudiation attacks. Moreover, the lower level of location privacy provided by the schemes demands further improvements. Therefore, we propose a novel pseudonym swap scheme that uses swappable and non-swappable pseudonyms to attain infrastructure independence while adhering to VANET security requirements. In this scheme, vehicles, independent of RSUs, cooperatively swap and change pseudonyms within mix-contexts having a high level of location privacy. Each exchange is then reported to the authority to enforce accountability and non-repudiation. Besides adhering to VANET security requirements, the simulation experiments show that our scheme outperforms existing pseudonym swap schemes, providing VANET users with a high level of location privacy.