Relating to the manuscript to which you linked, it is a similar story for other variant callers (samtools mpileup, GATK, etc) in the sense that they disagree on the calls that they make (and don't make). I'm not surprised, therefore, that somatic variant callers also differ. The authors particularly noted that sequencing depth had a major impact on variant calling, which is something that I also noted in my own analyses (greater depth is not necessarily better).
If you don't have a matched normal, then you can still call variants in your sample using the standard tools and then use available online resources for filtering out variants that are most likely not somatic (but this will not identify all of these such variants because most somatic variants will be private to the individual and thus not seen in any other individual), such as:
- dbSNP / ClinVar
- 1000 Genomes Phase III
- Exome Variant Server
- Greater Middle East
Remember, however, that if you are interested in how germline variants increase risk of cancer, then you don't want to be filtering these out just because they may be present in one of these databases listed above. These large-scale sequencing projects don't contain true healthy controls and each of these individuals that partook in these studies carry their own inherited risk factor alleles (even hg19 / GRCh37 is not a 'healthy' reference genome, and neither is hg38 - no true healthy genome exists).
You can also filter your data against cancer-specific data in order to increase likelihood that they are indeed somatic, such as:
For both TCGA and ICGC, download the level 3 / open access data and build your own dataset for filtering.
Finally, you can annotate your variants with in silico prediction tools (don't just use one) in order to further refine the list to include only those likely to be pathogenic. You will find, however, that that majority of somatic variants are just 'passenger' variants and won't actually modify anything. It is the key 'driver' variants that you ought to find, which will make the genome or cell cycle (or something else) unstabe and that would have resulted in the cells becoming neoplastic.
Edit 20th June 2018: see this list for in silico pathogenicity / functional impact predictors: A: pathogenicity predictors of cancer mutations