If by Cv you mean coefficient of consolidation, or as Ginger has suggested coefficient of volume compressibility, the simple answer to your question is no, although you may be able to find some empirical correlations, of dubious accuracy, which will be quite dependent I am sure on your estimate of the over consolidation ratio.
A hand pentrometer purports to measure unconfined compressive strength (referred to as Qu typically). Vane measurements yield undrained shear strengths (referered to as Su or Cu typically).
Unconfined compressive strength is one half of undrained shear strength.
I have used the hand penetrometer frequently in both normally consolidated clays and in heavily over consolidated tills. The vane is the preferred field instrument, however the large amount of stone in the tills makes it necessary to use other means. I have found that the penetrometer shows reasonably close agreement to the results of unconfined compressive testing.
I have not subjected this to any statistical analysis, but think I am accurate in stating that the penetrometer results agree, within 25% to 50%, to the results of Qu testing, when performed on tills.
Having said all this, however, I would not think of the results as anything more than a strength index, and would not stretch the results to the extreme of using them for consolidation or compressibility parameters.