If there isn't a notched spacer between the top and bottom caps it is sometimes possible to put a wrench on the top cap and screw it down if both the top and bottom caps are slightly loose, this will also sometimes result in the two being better snugged together as well as the headset tighter, beware over tightening unless you have a combination wrench or headset wrench and you've stated you don't have the latter. If the two are well snugged together I've had luck using the 16pt end of a combination wrench by dropping it over both the top and bottom caps together and turning them both at once, with a 16pt end you double the odds of the wrench fitting over both at once and as wrenches always have a bit of slop to them the two caps don't have to be perfectly aligned. Down side to this idea is do you have the 36mm wrench you will need for that size headset? Being an 1 1/8 you'll need a 36mm wrench, park sells a nice double ended spanner for 32mm/36mm which are the two most common modern to semi-modern sizes. Many people like to use 2 headset wrenches, I find it hard to control the top one, some like an adjustable for the top cap but they have a tendency to slip and round off the corners of the headset, I prefer to have a 32mm and 36mm combination wrench(there are very close standard sizes that match more then good enough) since I can get it over the whole of the too cap, they don't slip or round things off, and they make great persuaders on loosening old stems. Just leave the T handle allen wrench in the stem fixing bolt once loose and whack it with the end of the wrench, stem with one or two hits moves easily.