Feasibility studies are usually not powered and that's why the number of study participants is not critical. Most of the time this study phase is used to demonstrate safety, proof of concept or practicality. The number of participants depends on the project and also how much funding and resources are available - but obviously: the more, the better. We have performed feasibility studies with n=5,10,20 participants. After completion of the feasibility studies, we usually perform power calculations in order to find out how many participants are needed to demonstrate efficacy and statistical significance.
As Marianne suggested, you would benefit from a consultation with a biostatistician, especially because you seem to be on your own. The sample size depends on the difference between the variable(s) that interest you. If this difference is substantial, a smaller group size will suffice, as you can imagine.
If the difference between the variables of interest tends to be small, it is far more important to pick the size of group that will give you useful information.
I would agree with Peter. We use pilot studies (n=10-20) not to test hypotheses, but rather to generate hypotheses and to get data to predict the power function. We typically recommend pilot studies to sponsors suggesting that before they invest large sums of $ in a clinical trial, they pre-test their product or intervention under open-label conditions that are most likely to produce positive results. If the product doesn't work under these open-label conditions, it is highly unlikely that it will work under the more controlled conditions of a clinical trial suggesting the need for re-evaluation. lf the product appears to work, it may be useful to include a discussion of the pilot study in the Technical Report or manuscript making it clear that it was conducted as a pilot study and the data were not used in the clinical trial..