Any suggestions appreciated
The easy fix, is to find a USB DVD drive, and use that, but that isn't going to work if you can't boot from USB (are you sure? check the BIOS carefully).
Years ago, I did create an eCS installer boot, on a CD drive, but that isn't as easy with ArcaOS, although it should work if you put the actual installer onto a USB stick (haven't tried it). Some major messing around would be required. I suspect that you would need to use the USB boot support, installed to a bootable CD, then put the actual installer (the ISO file) onto a USB stick. The initial boot (from CD) would need to load the boot stuff (to MEMDISK), and boot from it. After it boots, it will search for the ISO file (should find it on a USB stick), and mount that (in ISOFS) to do the actual install.
As Dave suggested, you can make a (slightly smaller than 2 GB) partition on the HDD, and follow the instructions. The "problem" with that is that you cannot prepare the drive, while you are booted from it. It can probably be done by booting DFSEE from a CD, then boot from the HDD.
Trying to replace a CD drive with a DVD drive, in a laptop, can be a real problem. They aren't all the same (physically), so you would need to find one that fits, and, from what I have seen, new DVD drives are expensive, and hard to find. Used are probably discarded for some reason. You probably also need an IDE DVD drive, which is even harder to find. Worse, it may have a proprietary interface, which probably doesn't exist for a DVD drive.
As suggested, connecting the drive to a system with a DVD drive (or boot support for a USB stick) is probably the answer. You may need a system that will support IDE, and figure out how to attach the power to the disk. I don't think it will allow you to install to a removable drive.
Another option, is to clone an existing boot drive to the HDD, using DFSEE. Again, you will need to find a way to attach the drive, so you can clone it.
Have fun...