Sleep spindles are critical in characterizing sleep and have been associated with cognitive function and pathophysiological assessment. Typically, their detection relies on the subjective and time-consuming visual examination of electroencephalogram (EEG) signal(s) by experts, and has led to large inter-rater variability as a result of poor definition of sleep spindle characteristics. Hitherto, many algorithmic spindle detectors inherently make signal stationarity assumptions (e.g., Fourier transform-based approaches) which are inappropriate for EEG signals, and frequently rely on additional information which may not be readily available in many practical settings (e.g., more than one EEG channels, or prior hypnogram assessment). This study proposes a novel signal processing methodology relying solely on a single EEG channel, and provides objective, accurate means toward probabilistically assessing the presence of sleep spindles in EEG signals. We use the intuitively appealing continuous wavelet transform (CWT) with a Morlet basis function, identifying regions of interest where the power of the CWT coefficients corresponding to the frequencies of spindles (11-16 Hz) is large. The potential for assessing the signal segment as a spindle is refined using local weighted smoothing techniques. We evaluate our findings on two databases: the MASS database comprising 19 healthy controls and the DREAMS sleep spindle database comprising eight participants diagnosed with various sleep pathologies. We demonstrate that we can replicate the experts' sleep spindles assessment accurately in both databases (MASS database: sensitivity: 84%, specificity: 90%, false discovery rate 83%, DREAMS database: sensitivity: 76%, specificity: 92%, false discovery rate: 67%), outperforming six competing automatic sleep spindle detection algorithms in terms of correctly replicating the experts' assessment of detected spindles.