sgml to xml

Hi

I am not sure if this is the right place for this question so please
bear with me. Here is my question.

I have some data that has an SGML DTD, but the data itself is
'XMLized". It still follows the SGML DTD as far as inclusions and
exclusions go. But it is well-formed data.

I want to write an XSLT for this data to convert into XML which
conforms to a schema.

Now I am thinking that I don't have to run this data through any SGML
-> XML converters can run the transformation on this data as is. I
still have to modify the DOCTYPE declarations to include SYSTEM
identifiers vs. PUBLIC.

Can the experts advice if my approach and thinking is right here?

Thanks
ak