one advantage of my will summary database is I can seach for terms - I would have noted any use of illegitimate, base + natural - between 1750 and 1800 there are some 10,000 wills of which I have summaries for somewhat over 4000 thus I claim a representative fraction. I have also looked at many parish regs for notes.
Natural as used in some Manx registers has the meaning of mentally deficient (a couple of women who produced illegitimate children were described as 'naturals', other children as natural idiots.
Base born is reasonably common in Parish regs though most parish clerks used illegitimate (Wm Walker once described one woman as fornacatrix - 1st time I'd ever seen that used) but I have only 1 will in which term is used
Acknowledgemnt of an illegitimate child in a child is very rare (somes words like son of .. known as ..) I have I think only 3 or 4 (two are grandchildren) examples in the period, and about the same number where the term is used by the court. Some form of words such as A son of B known as C is used in a couple more wills to indicate illegitimacy - several decrees use the word however.

Besides the will under discussion there are 5 others using 'natural' I have noted - one states natural born idiot , another natural + lawful father, another natural son (not sure re illeg), another natural dau of mother (illeg)

In the 1753 will a quater ox was left between son-i-law + natural son but the agreement says "And in case their Brother Jon Kirmeen has a legal right to the sd Quarter of the Ox," - rather strange as explicitly mentioned ?