There are 2 ways:
1) Use Matlab or Python for loading, modifying and writing dfsu files. Among other tools which might come in handy, the dfs libraries for free download here: https://www.mikepoweredbydhi.com/download/mike-by-dhi-tools
2) If manual modifications would be feasible, then I suggest to think of it as a 2-step procedure: (i) Run the simulation with constant evaporation/precipitation and write the items as outputs. (ii) modify the output file so that it serves as input for the next (final) simulation.
When doing (i), make sure that in the output file you have the right number of timesteps. You could do a short simulation with very short timesteps and then change the time step size of the output in the "Data utility". To find Data Utility: (a) open MIKE Zero, (b) click on "File"->"Options"->"Data Utility..." and (c) load the dfsu file. Once the file is prepared, you would need to modify the values in the different timesteps of the dfsu file.
Hope it gets you one step further.
Stefan