One normally gets drivers from the manufacturer, in this case of the pen drive. Try their website. If they have no 95 driver, you might try a 98 driver, but there is some danger in that.
I agree with one of the previous replies that temporarily connecting the hard drive as a slave in the new PC is most likely to succeed. Be sure to set the jumpers to "slave". If you need info on the jumper settings, go to the the hard drive manufacture's web site.
Other options that might work include:
1. Mount a ZIP-100 drive in the old PC. Iomega still offers drivers for win95 machines. Unfortunately, unless you can get one used, ZIP drives and disks tend to be pricy. Also, you would then need to connec tthe same drie to the new PC, at least temporaril. To be clear, the ZIP dos not need to fit inside the PC (portable you said?). It only need to be connected to power and an IDE signal connector.
2. Try a bootale rescue CD, most of which are LINUX based. These can boot a PC into a version of LINUX more modern than 1995, thereby bypassing some of the win95 limitations. Such rescue CDs come with their own drivers, and can run CD burning software, USB, etc. BUT, their use is predicated upon being able to set the BIOS of the PC to boot from CD.
My favorite rescue CD is KNOPPIX. That is a big, full-featured program that is offered as a free download in the form of a 700 Meg ISO image. They also offer a multi-Gig DVD ISO image. You could try the CD image, but first read their minimum hardware requirements.http://www.knoppix.org/
There is a mini-KNOPPIX at: http://www.inittab.org/lite.html
Other, smaller, free rescue CDs include. Some will work on win95 era computers:http://trinityhome.org/trk/http://www.inside-se.../insert_en.htmlhttp://www.avast.com...st_bart_cd.htmlhttp://frenzy.org.ua/eng/http://www.tux.org/p.../looplinux/rip/http://repairlix.sourceforge.net/
HINT: If you want to try to use the USB pen drive, be sure to plug it into the computer BEFORE booting from any of these rescue CDs.