That's right. Negative Fst values should be effectively seen as zero values. A zero value for Fst means that there is no genetic subdivision between the populations considered. Then the high P-value, which indicates non statistically significant differences in the frequencies of the marker examined between the targeted populations.
Can the high P-value be the result of inadequate sampling size (n = 10)? Or what other reason might there be, especially since comparison between other populations (also n = 10) was significant...
The high p-value means that this is not significantly different from the divergence you might obtain if the samples were taken from the same population. It means you can ignore this result (if the p value was low, then you would need to ask why).
Despite the recommendations given, the negative values of Fst, Gst, G´st, D and their versions adjusted for sample bias should not be considered as zero values. Gerlach et al. (2010) through simulations showed that it is an error of very small sample sizes with a large size of alleles. The standard deviation associated with these values is very large. For example, D values = -0.181 ± 0.56 SD but the single values ranged from -1.47 to 0.49. It is suggested to increase the sample thus eliminating negative values.
Gerlach G, Jueterbock A, Kraemer P, Deppermann J, Harmand P. Calculations of population differentiation based on GST and D: forget GST but not all of statistics! Mol Ecol. 2010 Sep;19(18):3845-52. doi: 10.1111/j.1365-294X.2010.04784.x. Epub 2010 Aug 23. PMID: 20735737.