You will probably save time taking the radiator out if it is relatively easy to do. On my older tractor there were two lock plates and four bolts holding the fan on. They were sunken into the fan and could not be seen from above or sides since the fan shroud extended a bit past the fan.
Removing the hood took about ten minutes and taking the radiator off took about another ten or fifteen minutes since I didn’t want to cut the hoses off so struggled with them a bit. After that getting the fan off and back on took about five minutes (fan tips had been damaged before I bought the tractor).
Your tractor seems to have some foam seals around the radiator that might need to be replaced if they are old and fragile so that might make it more trouble and expensive to remove the radiator. You may consider getting some inexpensive snake style camera to get a view of the fan bolts and how to remove them.
Good luck!