Here your company wants to increase employee engagement and therefore wants to include picnics,get togethers as a way of increasing morale and interaction on social basis.There are several such extra activities which can be planned-games,hiking etc.
So instead of restricting the employee engagement activities by specific actions like outing,picnic,you can mention that the company would like to foster good relations,deepen employee engagement and special activities would be included in the programme.
A policy decision can be taken to incorporate employee engagement activities as a part of company routine.
"Employee Engagement and recreational program" seems good... Any way, it's just a fancy name for "Team building". Keep this for the annual outing, & thinki something different for the half yearly dinner. May be seperate policy sections would help keep these two events detached from each other.
But if you make it a policy, then it has to be followed every year at defined intervals... It will be audited & compliance to all your quality norms (ISO, OHSAS, etc) will have to be considered in planning these events.
Bye the way, It's a very good initiative & such "engagement & recreational programs" need to be really considered in policies. Congrats on initiating it in your organisation....