The Longman entry for prevent shows "from" in parentheses, which I understand to mean optional.
I'd say yes, it's correct without "from", but with "from" is the most natural / common sounding to my ears. If I leave out "from," I would use the possessive "our": ...."shouldn't prevent our trying to devise...."
A similar example:
"...and prevent our having to rely so much on foreign borrowing," (CNN 1990)
"A shred of regulative use suffices to prevent our completing the transition"
(CONSTITUTIVE RULE SYSTEMS AND CULTURAL EPIDEMIOLOGY. 2001)