These suggestions are based on your comment that you have the gene sequence.
For a statistical approach, you could formulate a null model and show that the sequence similarity you observe is much higher than expected under the null model, but reasonable under your exon shuffling model. Ideally, you would show this individually for each exon, to convince the reader about the exons' disparate origins. I'll propose a reasonable null model, though suggestions are gladly accepted here. Pick a random gene, assume it's built using exon shuffling, and search the rest of the transcriptome for sequences that best substantiate that argument.
For an evolutionary approach, you could search for orthologs (homologues? I never remember the difference) of your gene in other species. Hopefully, the results would show that your gene formed more recently than the exons it's built out of. If your gene actually has some other origin, maybe you'll find out it's older than some of its putative components. This can't exactly "confirm" your hypothesis, but it will test your hypothesis and just be generally a cool thing to try.