How to remap keys under Linux for a specific keyboard only

Yes, it's possible using XKB. Unlike xmodmap, XKB can remap your keys for individual devices.

Note: Make sure you have xkbcomp > 1.2.0

First list your devices with:

xinput list

You'll get something like this:

⎡ Virtual core pointer                      id=2    [master pointer  (3)]
⎜   ↳ Virtual core XTEST pointer                id=4    [slave  pointer  (2)]
⎜   ↳ Wacom Bamboo Pen Pen stylus               id=11   [slave  pointer  (2)]
⎜   ↳ Wacom Bamboo Pen Finger touch             id=12   [slave  pointer  (2)]
⎜   ↳ Logitech USB-PS/2 Optical Mouse           id=13   [slave  pointer  (2)]
⎜   ↳ Wacom Bamboo Pen Pen eraser               id=14   [slave  pointer  (2)]
⎜   ↳ Wacom Bamboo Pen Finger pad               id=15   [slave  pointer  (2)]
⎜   ↳ GASIA USB KB V11                          id=17   [slave  pointer  (2)]
⎣ Virtual core keyboard                     id=3    [master keyboard (2)]
    ↳ Virtual core XTEST keyboard               id=5    [slave  keyboard (3)]
    ↳ Power Button                              id=6    [slave  keyboard (3)]
    ↳ Power Button                              id=7    [slave  keyboard (3)]
    ↳ G19 Gaming Keyboard                       id=8    [slave  keyboard (3)]
    ↳ G19 Gaming Keyboard                       id=9    [slave  keyboard (3)]
    ↳ Logitech G19 Gaming Keyboard              id=10   [slave  keyboard (3)]
    ↳ GASIA USB KB V11                          id=16   [slave  keyboard (3)]

Identify the string of your device and edit the following shell script, changing the sed line with one that fits your device's name. Then change the keys you need remapped.

Example: Load xev and press a key you want to remap. Suppose you find out it's keycode 84. Lookup 84 in https://gist.github.com/zoqaeski/3880640. The key name there is <KP5>. Then lookup the key you want it replaced by (in the same link, farther below) and copy what's inside the brackets. Repeat the process for all the keys you want.

remote_id=$(
    xinput list |
    sed -n 's/.*GASIA.*id=\([0-9]*\).*keyboard.*/\1/p'
)
[ "$remote_id" ] || exit

# remap the following keys, only for my custom vintage atari joystick connected
# through an old USB keyboard:
#
# keypad 5 -> keypad 6
# . -> keypad 2
# [ -> keypad 8
# left shift -> left control

mkdir -p /tmp/xkb/symbols
# This is a name for the file, it could be anything you
# want. For us, we'll name it "custom". This is important
# later.
#
# The KP_* come from /usr/include/X11/keysymdef.h
# Also note the name, "remote" is there in the stanza
# definition.
cat >/tmp/xkb/symbols/custom <<\EOF

xkb_symbols "remote" {
    key <KP5>  { [ KP_Right, KP_6, U2192, U21D2 ]       };
    key <I129> { [ KP_Down, KP_2, U2193, U21D3 ]       };
    key <AD12> { [ KP_Up, KP_8, U2191, U21D1 ]  };
    key <LFSH> { [ Control_L ]        };
};
EOF

# (1) We list our current definition
# (2) Modify it to have a keyboard mapping using the name
#     we used above, in this case it's the "remote" definition
#     described in the file named "custom" which we specify in
#     this world as "custom(remote)".
# (3) Now we take that as input back into our definition of the
#     keyboard. This includes the file we just made, read in last,
#     so as to override any prior definitions.  Importantly we 
#     need to include the directory of the place we placed the file
#     to be considered when reading things in.
#
# Also notice that we aren't including exactly the 
# directory we specified above. In this case, it will be looking
# for a directory structure similar to /usr/share/X11/xkb
# 
# What we provided was a "symbols" file. That's why above we put
# the file into a "symbols" directory, which is not being included
# below.
setxkbmap -device $remote_id -print \
 | sed 's/\(xkb_symbols.*\)"/\1+custom(remote)"/' \
 | xkbcomp -I/tmp/xkb -i $remote_id -synch - $DISPLAY 2>/dev/null

Then source it (you can add it to your .xinitrc). All done! Now pressing the keys should generate the desired output, only for the device you specified.

Edit: Recently, I've noticed that, for some reason, the new configuration isn't applied immediately. You must first press a key on your other keyboard, then test the configured keys on your modified keyboard. I don't know why this happens, maybe some sort of cache.

For anyone else who's coming here off Google and wants an answer more in line with what the questioner was originally hoping for, I am aware of two ways to remap events at the evdev level so that the change applies to all applications:

1. udev provides an API for modifying the hardware database entries which control the mappings between scancodes and keycodes. This ArchiWiki page, which contains instructions, explicitly says that it'll work for both X11 and console input.

   The gist is that you create a custom entry in /etc/udev/hwdb.d/ which consists of a device match pattern and some scancode-to-keycode remapping definitions, then run systemd-hwdb update to rebuild the database and udevadm trigger apply it without a reboot.

2. Given that Wayland doesn't use X11's keyboard subsystem and major Wayland compositors like GNOME Shell and Weston don't implement UIs to configure the relevant aspects of libinput, someone wrote a daemon named evdevremapkeys which resolves the problem similarly to the G15Daemon userspace driver for Logitech G15 gaming keyboards.

   (It swallows events it intends to remap, so nothing else listening on the device can see them, then emits the corrected events via the uinput API for creating kernel-level input devices from userspace.)