I have never heard of a way to strip individual files off an image. If you have more than 16MB on different partitions, you could combine that, or, as you mentioned yourself, get more flash on a PCMCIA (e.g. a 20MB PCMCIA card).
What is the image name you want to install anyway ?
I actually just searched the IOS download page for the specs, but there also is a tool that lets you type in the image name and then gives you all the memory requirements, as well as the supported features. You do need a certain privilege level though to access that tool, here is the link (you will get prompted for a username and password):
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...