  Ta/CoFeB/MgO trilayers with perpendicular magnetic anisotropy are often
characterised by vanishing or modest values of interfacial
Dzyaloshinskii-Moriya interaction (DMI), which results in purely Bloch or mixed
Bloch-N\'eel domain walls (DWs). Here we investigate the creep evolution of the
overall magnetic bubble morphology in these systems under the combined presence
of in-plane and out-of-plane magnetic fields and we show that He$^+$ ion
irradiation induces a transition of the internal DW structure towards a fully
N\'eel spin texture. This transition can be correlated to a simultaneous
increase in DMI strength and reduction in saturation magnetisation -- which are
a direct consequence of the effects of ion irradiation on the bottom and top
CoFeB interfaces, respectively. The threshold irradiation dose above which DWs
acquire a pure N\'eel character is experimentally found to be between 12
$\times$ 10$^{18}$ He$^+$/m$^2$ and 16 $\times$ 10$^{18}$ He$^+$/m$^2$,
matching estimations from the one dimensional DW model based on material
parameters. Our results indicate that evaluating the global bubble shape during
its expansion can be an effective tool to sense the internal bubble DW
structure. Furthermore, we show that ion irradiation can be used to achieve
post-growth engineering of a desired DW spin texture.
