As you have not had a reply yet I will suggest a method (untried!)
1. As you state slice up the new USB stick as per your old one.
2. With Solaris at this point you would run a command to install the boot block into slice 0, for Linux you either go to a desktop system with the same distro in and and select (System -> Administration -> Create a USB startup disk) or you might try this:
Free Utility To Make Your USB Pen Drive Bootable | Megaleecher.Net
3. Mount up each slice in turn from your stick and the new one (e.g. to .mount/source and /mount/target).
4. Copy with:
find /mount/source | cpio -pdmv /mount/target.
Let the forum know how you get on?
HTH