Most honing seems to be done with cheap tools that scratch the bore and leave it in a considerable mess, especially if you don't have a way to rotate them at around 200 rpm so you can pump it up and down the bore fast enough to get the desired 30 degree cross hatch of hone marks. If you have a bench drill you can make a simple hone out of a wooden cylinder barely smaller than the bore, so it fits very easily down the bore when the drill's motor is not running. Use a nearly-radial saw cut down the full length of the cylinder to anchor one end of a suitable sheet of abrasive paper, cut to just barely make one circumference of the cylinder (not counting the bit that goes into the anchor slot) without overlap. By rotating it as slowly as your drill will run (which is fairly slowly if it is a double-reduction type of drill), whipping the drill handle up and down rapidly with one hand, and trickling kerosene down the bore with the other hand, you can get a professional job, without buying a tool that isn't any good anyway.
So far I'm finding it easy to remove mower engine valve springs with my fingers if they have the keyhole style of retainers, which most Briggs and Honda engines do. You can also use Joe Carroll's method, which involves a pair of plastic cable ties, positioned on opposite sides of each spring.
With regard to the valve chest cover, remember it is also the Positive Crankcase Ventilation valve, and it probably has metal swarf inside it so it needs to be cleaned out properly.
