To avoid creating large intermediate files, you might try running fastuniq with named pipes.

To set up the pipes:

$ mkfifo example.pair1.fastq.gz.pipe
$ mkfifo example.pair2.fastq.gz.pipe
$ gunzip -c example.pair1.fastq.gz > example.pair1.fastq.gz.pipe &
$ gunzip -c example.pair2.fastq.gz > example.pair2.fastq.gz.pipe &

Set up a list of filenames from the named pipes:

$ cat pipelist.txt
example.pair1.fastq.gz.pipe
example.pair2.fastq.gz.pipe

Then run fastuniq with your list and options:

$ fastuniq -i pipelist.txt ...

When you are done, delete the pipes:

$ rm example.pair*.fastq.gz.pipe

Not all binaries accept named pipes, though, so this may not work. But it might be worth trying.

As FastUniq requires a list of files as input, only by decompressing the files you could use it. You could use another tool, such as Dedupe from BBTools, or SuperDeduper, both accept .gz files as input.

If it doesn't support zipped files there is no way around this. Your best approach is to unzip the file, pipe the data into fastuniq, then zip the output. For example:

gunzip sample.fastq | fastuniq | gzip -c > uniq.fastq.gz