German to English Law/Patents Law: Contract(s)

I am revising a translation of a real estate contract with reference to Auftraggeber and Auftragnehmer, translated as customer and contractor which is fine
However, in sentences such as
Der AN ist verpflichtet, bei Erfüllung der ihm nach dem jeweiliger PV obliegenden Leistungen ....
ihm is translated as "they"
The CO shall be obliged, on completion of the services incumbent upon them according to the appropriate PA

This is a question I often have to deal with the gender problem of German words
e.g. - der Auftragnehmer - er , ihm usw.
In a US English contract would you refer to the contractor and then him/his or their ?
I can't add a whole paragraph about gender neutrality and putting him/her in all the time is also not possible here.
How would you deal with this. The contractor - they - strikes me as wrong but him might be "sexist". Do I have to worry about that in a contract?
This is obviously not the only sentence
e.g.
Insbesondere verpflichtet sich der AN personenbezogene Daten, die ihm im Zusammenhang .....
In particular, the CO shall be obliged to process and use personal data, which has come into their hands in conjunction with....

Thanks for your thoughts

Wendy