Yes, you can use a cake pan as a frying pan. I have done so twice in the past 40 years because I decided to do some frying while out. In my case, a steak with fresh fried potatoe/onion/green pepper for supper, and, a half dozen scrambled eggs/bacon for breakfast on a zero day. I picked up a cheap aluminum cake pan to cook on.
The flame spreader is probably not needed. Typicaly, I simply dented in the bottom to make a "dished" bottom. The dished bottom seems to trap heat from a lower flame and spread it out along the bottom a bit better than leaving it flat. It changes the heat area from about 1-1/2" to about 3". 'Corse I used a wind screen to insure that the heat "puddle" was not disrupted. A small amount of oil was used to cook the steak, you may need a bit more with less fatty foods like trout. The non-stick coating on the cheap pans is very thin. Some gravelly sand will usually get the worst of it out, though it works OK the first time out. I added parified butter to cook the potatoe/onions and pepper before frying the steak. I was using the older Coleman F1 stove at the time. Since, I have gone back to a SVEA. After eating, I simply dumped in about a 1/4 liter of water and let it sit about 20min. All the residue came out easily with the piece of scrubbie and two drops of soap.
The second time I could only get a cheap steel pan. We made fried eggs and bacon that morning after a short hike up to a lake. That evening we had trout. Using the SVEA, I again bented the pan in, and cooked up the two trout by cutting them in half after removing the head/tail (the only way they would fit.) I used the aluminum foil as a lid to insure it was cooked fairly well...tapeworms and all that. The steel did not like to be dented and actually kinked around the edges. Again, a small amount of oil was used. This pan cost $1 at a dollar store as I headed up... Almost a throw away, it was put in the recycle bin after I got out.
If you happen to forget the fry pan, a cake pan can work pretty well.