It is a famous result due to Shelah that the consistency strength of perfect set property (i.e. every uncountable set of reals has a perfect subset) with $ZF+DC$ is the same as the existence of an inaccessible cardinal. Does Shelah's argument also answer the following question?

Question: Does the consistency of $ZF+DC+\mbox{ every non-null set has a perfect subset}$ imply the consistency of the existence of an inaccessible cardinal?