Yes, PCC would be the best option to oxidise the primary alcohol to an aldehyde because the aldehyde hydrate does mot form. However, we are experimenting with chromic acid specifically and in this case I'm asking if it would be possible to exclude sulphuric acid by not preparing the chromic acid through "standard" dichromate/sulphuric/water mix, but rather through CrO3 and H2O.
I understand that if the aldehyde is left exposed to H2O it will form the aldehyde hydrate and then will be further oxidised by the chromic acid like you say. If I make use of the volatility of the formed aldehyde (in this case ethanal BP ±22°C). I can prevent this from happening to a certain extent by keeping the reaction vessel well above the BP while implementing mechanical stirring, thereby removing acetaldehyde through vapour phase and then condensing it.