Yes, you could use a spectrum analyser and tracking gen here and get good results.
The other thing is that most people probably don't 'need' to make the classic (screened) H field probes from semi rigid cable. You can get fairly good results just using an open loop of wire. I have a boxful of various RF probes and sniffers here and one of my favourites is nothing more than a 'square' 2.5cm loop (2.5cm measured diagonally from corner to corner like a TV) made from some enamelled copper wire that is connected to some semi rigid cable as a loop connection across the inner and outer of the coax. You don't need to use semi rigid cable here either as ordinary cable will do but it won't be as stiff to hold as semi rigid cable so you lose the 'wand' feel to it all. This makes a quick and cheap H field probe.
The E field probe is just a regular bit of coax with just a few mm of the centre peeping out. So you could make both of these probes in a few minutes for next to no cost. Make several of the square H field loop variety in several sizes and you can do a lot of useful work. It's not going to be quite as good as the real thing but still a lot better than nothing