You need an 8bit 2 way changeover switch with 16 input bits. This changes from bits 0 to 7 to output to giving bits 8 to 16 to output. It could be just 2 banks of 8 way DIL switches.

You have to read the memory once, move all the switches over then read it again.

Then you need a processing routine to combine the 8 bit bytes into 16 bit words.

You can use electronic switches - it used to be done to read 8 bit memory bytes into the standard parallel printer port of an IBM PC, which had only 4 or 5 inputs - data was moved in two 4 bit nibbles. Modern PCs with bidirectional 8 bit printer ports can do it a byte at a time.

It depends how often and how quickly you want to do this.