Flash assembly to microcontroller
This is not an uncommon thing to do: you are looking for an assembler.  This can be done on any microcontroller.  All manufacturers provide tools to do this.  Often it is in the same package as those "high level" IDEs.  The IDE is merely running the command-line tools for you, whereas you will run them directly.

The easiest way to step into this is would be to use the standard bootloader and write your amount inline inside your C/CPP file using the "asm" directive.  Once you are practiced at it, you can then move to writing the assembly code in an .asm file and running the assembler instead of the C compiler.  Then you can skip the step of linking to the standard C libraries and standard bootloader, and flash the output directly to the microcontroller.

Supposing you chose Atmel, you could do this two ways:

The simplest would be to purchase a development board like the Arduino.  Next download the Arduino IDE to start with inline assembly.  Lastly download AVR Studio which is the full development platform.

The bare-metal way would be to purchase an Atmel microcontroller like the AtMega328p + a USB in-circuit programmer (ISP). Then download the AVR Studio.  Mount the chip on a breadboard and use the ISP to flash the chip using AVR Studio.

Hopefully I've given you enough keywords that you can find your way from here.