Would assigning a Project of a Bank to a Muslim subordinate be permissible ?

Assalamualaikum Mufti Saheb, I'll be grateful if you could answer the following question I'm working for a Software Development Organization as a Project Manager. Sometimes our company gets software development projects from clients whose income is not Halaal. For example.. Banks or Wine Manufacturing Companies etc. I'd like to know that if I am assigned to manage such a Project, would it be permissible for me to work on it. Sometimes there isnt another Project Manager available to whom the project can be assigned. More importantly, my job is to assign programming tasks of the project to Programmers working under me, quite a few of whom are Muslims. I'd like to know if I'd be committing a major sin if I assign a Programming Task on this project to a God-fearing Muslim employee working in my team.