The laptop you describe is unlikely to be able to support USB ports, for hardware reasons. But there may be an alternative solution.
The first USB standard (version 1.0) was published in 1996, but didn't really gain traction in the PC market until version 1.1 was released in 1998. The PCI bus standard had been published in 1992, and by the mid 1990s it was commonplace in new desktop machines (though often with old ISA slots alongside). As such, manufacturers concentrated on developing USB interfaces for the newer, faster PCI bus. It appears that no USB controller cards were ever developed for the ISA bus. In recent years, an ISA USB adapter has been developed, but this only allows you to use a USB flash drive as a replacement for a hard drive; it doesn't actually function as a full USB interface.
The relevance for your laptop is this: the PC Card (PCMCIA) standard, as far as version 4, was effectively a portable version of the 16-bit ISA bus. Version 5, also known as Cardbus, added a 32-bit standard, based on the PCI bus. This predated USB slightly, being published in 1995.
Because no USB interface chips had been designed for the ISA bus, PC Card manufacturers would have chosen to make 32-bit (Cardbus) cards using existing PCI-oriented chips, instead of designing their own chips from scratch for a 16-bit card. In the late 1990s, few people would have wanted to spend money on adding USB ports to an old ISA-based laptop: they'd be more likely to use their cash to get a new laptop.
To the best of my knowledge, no 16-bit USB interface cards were ever manufactured.
Hardware issues aside, Windows 95 was the first MS operating system to include USB support, as an add-on in the OSR 2.1 version. The implementation is rather basic (with limited driver support), and the provision in Windows 98 was much improved. DOS support was much more limited, but support for pendrives improved in recent years, as people doing BIOS updates on newer machines have had to support booting DOS (and the update software) from a USB drive rather than a floppy disk.
If your main requirement is to transfer files to/from your laptop, you may wish to consider using a CompactFlash card instead. These can be inserted into a 16-bit PC Card slot using a passive adapter, so would work fine on your laptop. It would be treated by Windows as a regular PC Card. and Windows 95 has built-in drivers that will allow you to read/write the card, and hotplug (insert/eject) it safely. The same may be possible under DOS, but it would require finding DOS drivers for your laptop's PC Card (PCMCIA) controller first.