Is it possible to create a ketone using ozonolysis, when you have an alkene with no alkyl groups?
I don't think that's possible. 

The general reactions scheme for ozonolysis is as follows: 

Consider the case of butene: 



Herein $R_1$ and  $R_3$ can be identified as methyl groups, and similarly $R_2$ and $R_4$ are plain old hydrogens. Following the reaction scheme, one would naturally expect Ethanal as a product (if you use $\ce{Zn}$, ethanoic acid may be obtained if you use something else).

I'll drop by later and write out a mechanism perhaps.