Yes, you can change the oil and not change the filter, but I'd suggest not running the new oil with the old filter as long as your normal interval. As my recent oil analysis showed, the oil, especially full synthetic, can go longer than the 5,000 miles I usually run. Years ago carmakers recommended changing oil and filter at certain intervals and had different recommended interval for changing the oil but not the filter every other time. When Mobil 1 first came out they advertised you could run longer change intervals than conventional oil.
I changed mine once when we were on a long trip. I put the used oil in jugs with screw caps, put the filter in a zip lock bag, and placed them along with the dirty pan in a big plastic bag. I disposed of everything properly when I got home.
Here's a thought. To get an idea about whether or not you really need to change the filter, the next time you change it, cut open the filter. How much crud is in it? If it has plenty of filter capacity left, you should be fine to skip a filter change. If it's pretty much full, don't risk it.
2011 Sunseeker 3100
1997 Pathfinder Toad