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Yes, you can use an expression tree walker:

from sage.symbolic.expression_conversions import ExpressionTreeWalker

class SubstituteNumericalApprox(ExpressionTreeWalker):
    def __init__(self, **kwds):
        """
        A class that walks the tree and replaces numbers by numerical
        approximations with the given keywords to `numerical_approx`.
        EXAMPLES::
            sage: var('F_A,X_H,X_K,Z_B')
            sage: expr = 0.0870000000000000*F_A + X_H + X_K + 0.706825181105366*Z_B - 0.753724599483948
            sage: SubstituteNumericalApprox(digits=3)(expr)
            0.0870*F_A + X_H + X_K + 0.707*Z_B - 0.754
        """
        self.kwds = kwds

    def pyobject(self, ex, obj):
        if hasattr(obj, 'numerical_approx'):
            return obj.numerical_approx(**self.kwds)
        else:
            return obj

Example usage:

sage: var('F_A,X_H,X_K,Z_B')
sage: expr = 0.0870000000000000*F_A + X_H + X_K + 0.706825181105366*Z_B - 0.753724599483948
sage: SubstituteNumericalApprox(digits=3)(expr)
0.0870*F_A + X_H + X_K + 0.707*Z_B - 0.754

Yes, you can use an expression tree walker:

from sage.symbolic.expression_conversions import ExpressionTreeWalker

class SubstituteNumericalApprox(ExpressionTreeWalker):
    def __init__(self, **kwds):
        """
        A class that walks the tree and replaces numbers by numerical
        approximations with the given keywords to `numerical_approx`.
        EXAMPLES::
            sage: var('F_A,X_H,X_K,Z_B')
            sage: expr = 0.0870000000000000*F_A + X_H + X_K + 0.706825181105366*Z_B - 0.753724599483948
            sage: SubstituteNumericalApprox(digits=3)(expr)
            0.0870*F_A + X_H + X_K + 0.707*Z_B - 0.754
        """
        self.kwds = kwds

    def pyobject(self, ex, obj):
        if hasattr(obj, 'numerical_approx'):
            return obj.numerical_approx(**self.kwds)
        else:
            return obj

    def __call__(self, ex):
        result = super().__call__(ex)
        return result.numerical_approx(**self.kwds) if result in CC else result

Example usage:

sage: var('F_A,X_H,X_K,Z_B')
sage: expr = 0.0870000000000000*F_A + X_H + X_K + 0.706825181105366*Z_B - 0.753724599483948
sage: SubstituteNumericalApprox(digits=3)(expr)
0.0870*F_A + X_H + X_K + 0.707*Z_B - 0.754
sage: SubstituteNumericalApprox(digits=5)(1.5*2^x/log(2))
2.1640*2.0000^x