I´m working with this dataset(GSE234297) that provides a salmon counts file and a salmon offsets file(GSE234297_gene_raw_counts.txt.gz GSE234297_gene_offset_matrix.txt.gz) . The paper authors use them like this to do DEG:~

 # create DGEList
y <- DGEList(counts = counts, samples = samples, genes = genes, group = samples$Disease_status)

# add salmon offsets
y <- scaleOffset(y, offset = as.matrix(salmon_offset)) 

# filter low count genes 
keep <- filterByExpr(y, group = y$samples$group)
table(keep) 
y <- y[keep, , keep.lib.sizes=FALSE] 

# set design matrix
design <- model.matrix(~ Sex + GC_content + group, data = y$samples)
design

# estimate dispersion parameters using edgeR robust method
y <- estimateGLMRobustDisp(y, design)

But my question is if I want to use the salmon offsets for Wilcoxon (which can't use offsets directly), could I simply do:

Copy <- DGEList(counts)
y$offset <- offsets  
cpms <- edgeR::cpm(y, offset = y$offset, log = FALSE)

To get properly normalized values that account for the Salmon bias corrections?

To compute CPM values from edgeR:

y <- DGEList(counts = counts, samples = samples, genes = genes, group = samples$Disease_status)
y <- scaleOffset(y, offset = salmon_offset) 
cpms <- cpm(y)

Needless to say, using edgeR v4 quasi-likelihood would be much faster and better than Wilcoxon tests. I would be skipping the estimateGLMRobustDisp call shown in your code above and instead using:

fit <- glmQLFit(y, design, robust=TRUE)
ftest <- glmQLFTest(fit)
topTags(ftest)

BTW, please ask questions just once. I answered essentially the same question from you 3 hours ago, added as a comment to an old answer.