Yes, there is a 'g' in those words. Apart from in a few regional accents, such as some accents in the southern states of the US, the 'g' is always pronounced. There is a clear difference in pronunciation between 'shavin' and 'shaving' . However, the sound is not the same as a regular 'n' followed by a regular 'g'. The 'ng' has a sound all of its own - it's a kind of combined consonant, written /ŋ/. It's a nasal sound, starting in the nose and released in the throat, but it's a softer 'g' than when 'g' occurs alone.

The 'G' is not intended to have a hard sound but to be almost French in its nasal quality. For example ShavING - the ING should be pronounced much like the ING in 'sing'. The G in the middle of a word will also be soft in words such as SinGing (singing) HanGing (hanging) Hope that helps Peter

G is never pronounced in -ing suffixes in spoken English. Instead it's replaced by the velar nasal consonant represented in IPA as [ŋ].