Yes, your cap is the only pressure relief you have. Make sure it is rated properly for your car. A pressure test of your cooling system will indicate if it is working properly or not. It also might indicate other problems with your cooling system and should be cheap to have performed.
As for the head gasket, sometimes pressurization of the cooling system from engine compression is only slight, if the point of failure is one that allows that flowpath.You require at least a compression test. (done wet and dry, to rule out rings). This is sometimes referred to as a cylinder leak-down check. The cylinder is allowed to pressurize, and you note if there is any drop in pressure over a period of time. In any cylinders that are showing leakage, you squirt some oil into the cylinder and repeat to see if either you get a higher compression figure, or the cylinder leaks less compression. If either occurs, it indicates ring problems. If the cylinder still leaks, and didn't show a slightly higher compression figure initially, the problem is related to the head in that cylinder, either valves not seating, or gasket. Removal of the head is the only realistic option at that point and a careful mechanic will look closely at the head gasket and will be able to determine the point of failure. I had a bad factory gasket on my Honda many years ago and removal indicated the point of cylinder charge tracking into the coolant.
You might be able to smell something in your coolant IF it is in fact head gasket related. You can also smell traces of coolant in exhaust long before you see the tell-take white smoke.
I don't mean to alarm you, but worst-case scenario is a cracked head, if indeed your hose problem is caused by overpressurization. It's a long chain of ifs that I have outlined, and some simple tests should show quickly if everything I have suggested is out to lunch or whether further digging is required.
You did examine the hoses to check what type of failure you were dealing with? A deteriorated hose you can probably tear by hand in other spots. In that case the fix is easy- just replace them all.