The Coronal Multi-channel Polarimeter (CoMP) has previously demonstrated the presence of Doppler velocity fluctuations in the solar corona. The observed fluctuations are thought to be transverse waves, i.e., highly incompressible motions whose restoring force is dominated by the magnetic tension, some of which demonstrate clear periodicity. We aim to exploit CoMP's ability to provide high cadence observations of the off-limb corona to investigate the properties of velocity fluctuations in a range of coronal features, providing insight into how (whether) the properties of the waves are influenced by the varying magnetic topology in active regions, quiet Sun and open field regions. An analysis of Doppler velocity time-series of the solar corona from the 10747 angstrom Iron XIII line is performe, determining the velocity power spectrum and. using it as a tool to probe wave behavior. Further, the average phase speed and density for each region are estimated and used to compute the spectra for energy density and energy flux. In addition, we assess the noise levels associated with the CoMP data, deriving analytic formulae for the uncertainty on Doppler velocity measurements and providing a comparison by estimating the noise from the data. It is found that the entire corona is replete with transverse wave behavior. The corresponding power spectra indicate that the observed velocity fluctuations are predominately generated by stochastic processes, with the spectral slope of the power varying between the different magnetic regions. Most strikingly, all power spectra reveal the presence of enhanced power occurring at similar to 3 mHz, potentially implying that the excitation of coronal transverse waves by p-modes is a global phenomenon.