The problem without running MRP is that you would not have any future planned requirements, so your CRP would only reflect W/O's that you have created. So if looking short term then CRP does not require MRP, but the results would not be very meaningful.
Actually getting the data set up for MRP is much easier than creating the routing data needed to get accurate CRP.
I believe you mentioned MRP run time is the issue you are trying to avoid.
If you need to calculate CRP for certain WC and only workorders you manually enter (MPS) it is an option. (Single level)
The CRP would use the data (prod time) from the routings and recalculate the capacity of workcenters and the routing production lead time based on the due date of the work order.
As output you get required capacity for WC's, if there are differences between mrp lead time (1.4.7) and routing calculated lead time (Time Fence Conflict) you will get a waring and WC's for finished Operations will no longer show that they require capacity.
Advantage: it is Fast. Con: remember the limitations!