In fact I think /sgul/ is a better transcription than /skul/ for someone who is familiar with a foreign language.
In English, the phonemes /g/ and /k/ are differentiated in two distinct ways. First, we use our voice box for the /g/ and not for the /k/. This is called "voicing." Second, we let a puff of air out on the /k/ and not on the /g/.
In fact, because these two are somewhat redundant, most English speakers do not voice the /g/ very strongly. Typically, the voicing begins only after the initiation of the consonant, in contrast to Spanish or French where the voicing begins right away.
In Spanish and French, /k/ and /g/ are differentiated only by voicing -- a puff of air is not used on either letter. As a result, English speakers often hear /g/ when second-language speakers from one of these languages intend /k/. (And the reverse happens when we try to learn one of these languages.) A similar story holds for /p/ vs. /b/ and also for /t/ vs. /d/.
(Contrast /s/ and /z/, where the only distinction is voicing -- there is no puff of air on the /s/. Here, English speakers do tend to voice the /z/ strongly and immediately.)
Now, the interesting thing about the "puff of air" is that we don't do if the consonant comes after an /s/. (So /sp/, /st/, and /sk/ are all unvoiced, and no air puff.) You might think we would then confuse these sounds with /sb/, /sd/, and /sg/, but luckily, these latter clusters do not occur in English words, so there is no risk of confusion.
Therefore your dictionary, which tells you to say /g/ after /s/, is half right and half wrong. It's right because you shouldn't puff the air, but wrong because you shouldn't use your voice box. Luckily the risk of misunderstanding here is very small, so if you were working on modifying "one step at a time" till you sound more like a native speaker, I would make this step very late in the process.