What's the difference between 1N4004 diode and 1N4007?
The main difference is the PIV rating (there are other somewhat subtle differences). If you are absolutely certain that more than 400VDC reverse bias is impossible in the circuit you can almost certainly use a 1N4004. Since there is little or no price difference between PIV ratings some may standardize on the higher voltage rated parts. 

1N4006 and 1N4007 are made differently from 1N4001-4005- they are actually PIN diodes and can even be (ab)used in RF applications as such, but I doubt that is a concern to you. There are also significant differences in forward and reverse recovery time (often not even typical numbers are given on modern datasheets).  See this answer, for example. 



Edit: Since you've added a schematic- I see no reason you can't substitute the lower PIV 1N4004.