You can define your own formatting like so:

ClearAll[pseudofraction]
Format[pseudofraction[x_, y_]] := FractionBox[x, y] // DisplayForm

or

Format[pseudofraction[x_, y_]] := FractionBox[x, y, Beveled -> True] // DisplayForm

when you want it beveled. Then

total = pseudofraction[3, 4] + 4

will be displayed as:

It looks like a fraction but it is internally not stored as a fraction:

FullForm[total]

gives:

Plus[4, pseudofraction[3, 4]]

Note that when you copy-paste it from a notebook, then it will be interpreted as a fraction, as that is the default meaning of a 'fraction box'.

Options[FractionBox]

gives:

{AllowScriptLevelChange -> True, BaseStyle -> {}, Beveled -> False, 
 DefaultBaseStyle -> {}, DenominatorAlignment -> Center, 
 FractionLine -> Automatic, MultilineFunction -> Automatic, 
 NumeratorAlignment -> Center, Overhang -> 0.25}

Note that all of them might not be implemented yet...

In hindsight, you could also do it like this:

ClearAll[pseudofraction]
Format[pseudofraction[x_, y_, opts___]] := FractionBox[x, y, opts] // DisplayForm
pseudofraction[2, 3] + 4 + pseudofraction[2, 3, Beveled -> True]